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vector-toc-level-2"> <a class="vector-toc-link" href="#Logics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Logics</span> </div> </a> <ul id="toc-Logics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Practice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Practice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Practice</span> </div> </a> <ul id="toc-Practice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a 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mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%B9%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%AE%E0%A6%BE%E0%A6%A8%E0%A6%A4%E0%A6%BE_(%E0%A6%95%E0%A6%AE%E0%A7%8D%E0%A6%AA%E0%A6%BF%E0%A6%89%E0%A6%9F%E0%A6%BE%E0%A6%B0_%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8)" title="সহবর্তমানতা (কম্পিউটার বিজ্ঞান) – Bangla" lang="bn" hreflang="bn" data-title="সহবর্তমানতা (কম্পিউটার বিজ্ঞান)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Samtidighed" title="Samtidighed – Danish" lang="da" hreflang="da" data-title="Samtidighed" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Nebenl%C3%A4ufigkeit" title="Nebenläufigkeit – German" lang="de" hreflang="de" data-title="Nebenläufigkeit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B1%CF%85%CF%84%CE%BF%CF%87%CF%81%CE%BF%CE%BD%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Ταυτοχρονισμός – Greek" lang="el" hreflang="el" data-title="Ταυτοχρονισμός" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Concurrencia_(inform%C3%A1tica)" title="Concurrencia (informática) – Spanish" lang="es" hreflang="es" data-title="Concurrencia (informática)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Konkurrentzia_(informatika)" title="Konkurrentzia (informatika) – Basque" lang="eu" hreflang="eu" data-title="Konkurrentzia (informatika)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D9%85%D8%B1%D9%88%D9%86%D8%AF%DB%8C_(%D8%B9%D9%84%D9%88%D9%85_%D8%B1%D8%A7%DB%8C%D8%A7%D9%86%D9%87)" title="همروندی (علوم رایانه) – Persian" lang="fa" hreflang="fa" data-title="همروندی (علوم رایانه)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%91%ED%96%89%EC%84%B1" title="병행성 – Korean" lang="ko" hreflang="ko" data-title="병행성" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Konkurensi_(ilmu_komputer)" title="Konkurensi (ilmu komputer) – Indonesian" lang="id" hreflang="id" data-title="Konkurensi (ilmu komputer)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Concorrenza_(informatica)" title="Concorrenza (informatica) – Italian" lang="it" hreflang="it" data-title="Concorrenza (informatica)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/Concurrency_(%D7%9E%D7%93%D7%A2%D7%99_%D7%94%D7%9E%D7%97%D7%A9%D7%91)" title="Concurrency (מדעי המחשב) – Hebrew" lang="he" hreflang="he" data-title="Concurrency (מדעי המחשב)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/P%C3%A1rhuzamoss%C3%A1g_(sz%C3%A1m%C3%ADt%C3%A1studom%C3%A1ny)" title="Párhuzamosság (számítástudomány) – Hungarian" lang="hu" hreflang="hu" data-title="Párhuzamosság (számítástudomány)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Keserentakan_(sains_komputer)" title="Keserentakan (sains komputer) – Malay" lang="ms" hreflang="ms" data-title="Keserentakan (sains komputer)" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Gelijktijdigheid_(informatica)" title="Gelijktijdigheid (informatica) – Dutch" lang="nl" hreflang="nl" data-title="Gelijktijdigheid (informatica)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%A6%E8%A1%8C%E6%80%A7" title="並行性 – Japanese" lang="ja" hreflang="ja" data-title="並行性" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Samtidighet_(informatikk)" title="Samtidighet (informatikk) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Samtidighet (informatikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Concorr%C3%AAncia_(ci%C3%AAncia_da_computa%C3%A7%C3%A3o)" title="Concorrência (ciência da computação) – Portuguese" lang="pt" hreflang="pt" data-title="Concorrência (ciência da computação)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Concuren%C8%9B%C4%83_(informatic%C4%83)" title="Concurență (informatică) – Romanian" lang="ro" hreflang="ro" data-title="Concurență (informatică)" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D0%B8%D0%B7%D0%BC_(%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Параллелизм (информатика) – Russian" lang="ru" hreflang="ru" data-title="Параллелизм (информатика)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Nj%C3%ABkoh%C3%ABsisht_(shkenca_kompjuterike)" title="Njëkohësisht (shkenca kompjuterike) – Albanian" lang="sq" hreflang="sq" data-title="Njëkohësisht (shkenca kompjuterike)" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Concurrency_(computer_science)" title="Concurrency (computer science) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Concurrency (computer science)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Rinnakkaisuus" title="Rinnakkaisuus – Finnish" lang="fi" hreflang="fi" data-title="Rinnakkaisuus" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Samtidighet_(datavetenskap)" title="Samtidighet (datavetenskap) – Swedish" lang="sv" hreflang="sv" data-title="Samtidighet (datavetenskap)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Ability to execute a task in a non-serial manner</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Concurrent computer" redirects here. For the company, see <a href="/wiki/Concurrent_Computer_Corporation" title="Concurrent Computer Corporation">Concurrent Computer Corporation</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For a more practical discussion, see <a href="/wiki/Concurrent_computing" title="Concurrent computing">Concurrent computing</a>. For other uses, see <a href="/wiki/Concurrency_(disambiguation)" class="mw-redirect mw-disambig" title="Concurrency (disambiguation)">Concurrency (disambiguation)</a>.</div> <p>Concurrency refers to the ability of a system to execute multiple tasks through simultaneous execution or time-sharing (context switching), sharing resources and managing interactions. Concurrency improves responsiveness, throughput, and scalability in modern computing, including: <sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_3-0" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_4-0" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_5-0" class="reference"><a href="#cite_note-:4-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Operating_system" title="Operating system">Operating systems</a> and <a href="/wiki/Embedded_system" title="Embedded system">embedded systems</a></li> <li><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed systems</a>, <a href="/wiki/Parallel_computing" title="Parallel computing">parallel computing</a>, and <a href="/wiki/High-performance_computing" title="High-performance computing">high-performance computing</a></li> <li><a href="/wiki/Database" title="Database">Database systems</a>, <a href="/wiki/Web_application" title="Web application">web applications</a>, and <a href="/wiki/Cloud_computing" title="Cloud computing">cloud computing</a></li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Related_concepts">Related concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=1" title="Edit section: Related concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Concurrency is a broader concept that encompasses several related ideas, including: <sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_3-1" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_4-1" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_5-1" class="reference"><a href="#cite_note-:4-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Parallel_computing" title="Parallel computing">Parallelism</a> (simultaneous execution on multiple processing units). Parallelism executes tasks independently on multiple CPU cores, while concurrency manages multiple tasks on one or more cores, switching between threads or time-slicing without completing each one. Programs may exhibit parallelism only, concurrency only, both parallelism and concurrency, neither. <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Parallelism_vs_concurrency.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Parallelism_vs_concurrency.png/220px-Parallelism_vs_concurrency.png" decoding="async" width="220" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Parallelism_vs_concurrency.png/330px-Parallelism_vs_concurrency.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Parallelism_vs_concurrency.png/440px-Parallelism_vs_concurrency.png 2x" data-file-width="962" data-file-height="245" /></a><figcaption>Parallelism vs concurrency</figcaption></figure></li> <li><a href="/wiki/Multithreading_(computer_architecture)" title="Multithreading (computer architecture)">Multi-threading</a> and <a href="/wiki/Multiprocessing" title="Multiprocessing">multi-processing</a> (shared system resources)</li> <li><a href="/wiki/Synchronization" title="Synchronization">Synchronization</a> (coordinating access to shared resources)</li> <li>Coordination (managing interactions between concurrent tasks)</li> <li><a href="/wiki/Concurrency_control" title="Concurrency control">Concurrency Control</a> (ensuring data consistency and integrity)</li> <li><a href="/wiki/Inter-process_communication" title="Inter-process communication">Inter-process Communication</a> (IPC, facilitating information exchange)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Issues">Issues</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=2" title="Edit section: Issues"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because computations in a concurrent system can interact with each other while being executed, the number of possible execution paths in the system can be extremely large, and the resulting outcome can be <a href="/wiki/Indeterminacy_in_concurrent_computation" title="Indeterminacy in concurrent computation">indeterminate</a>. Concurrent use of shared <a href="/wiki/Resource_(computer_science)" class="mw-redirect" title="Resource (computer science)">resources</a> can be a source of indeterminacy leading to issues such as <a href="/wiki/Deadlock_(computer_science)" title="Deadlock (computer science)">deadlocks</a>, and <a href="/wiki/Resource_starvation" class="mw-redirect" title="Resource starvation">resource starvation</a>.<sup id="cite_ref-cleaveland1996_7-0" class="reference"><a href="#cite_note-cleaveland1996-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Design of concurrent systems often entails finding reliable techniques for coordinating their execution, data exchange, <a href="/wiki/Memory_allocation" class="mw-redirect" title="Memory allocation">memory allocation</a>, and execution scheduling to minimize <a href="/wiki/Latency_(engineering)" title="Latency (engineering)">response time</a> and maximise <a href="/wiki/Throughput" class="mw-redirect" title="Throughput">throughput</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=3" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Concurrency theory has been an active field of research in <a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">theoretical computer science</a>. One of the first proposals was <a href="/wiki/Carl_Adam_Petri" title="Carl Adam Petri">Carl Adam Petri</a>'s seminal work on <a href="/wiki/Petri_net" title="Petri net">Petri nets</a> in the early 1960s. In the years since, a wide variety of formalisms have been developed for modeling and reasoning about concurrency. </p> <div class="mw-heading mw-heading3"><h3 id="Models">Models</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=4" title="Edit section: Models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A number of formalisms for modeling and understanding concurrent systems have been developed, including:<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <ul><li>The <a href="/wiki/Parallel_random-access_machine" class="mw-redirect" title="Parallel random-access machine">parallel random-access machine</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Actor_model" title="Actor model">actor model</a></li> <li>Computational bridging models such as the <a href="/wiki/Bulk_synchronous_parallel" title="Bulk synchronous parallel">bulk synchronous parallel</a> (BSP) model</li> <li><a href="/wiki/Petri_net" title="Petri net">Petri nets</a></li> <li><a href="/wiki/Process_calculi" class="mw-redirect" title="Process calculi">Process calculi</a> <ul><li><a href="/wiki/Calculus_of_communicating_systems" title="Calculus of communicating systems">Calculus of communicating systems</a> (CCS)</li> <li><a href="/wiki/Communicating_sequential_processes" title="Communicating sequential processes">Communicating sequential processes</a> (CSP) model</li> <li><a href="/wiki/%CE%A0-calculus" title="Π-calculus">π-calculus</a></li></ul></li> <li><a href="/wiki/Tuple_space" title="Tuple space">Tuple spaces</a>, e.g., <a href="/wiki/Linda_(coordination_language)" title="Linda (coordination language)">Linda</a></li> <li><a href="/wiki/SCOOP_(software)" title="SCOOP (software)">Simple Concurrent Object-Oriented Programming</a> (SCOOP)</li> <li><a href="/wiki/Reo_Coordination_Language" title="Reo Coordination Language">Reo Coordination Language</a></li> <li><a href="/wiki/Trace_monoid" title="Trace monoid">Trace monoids</a></li></ul> <p>Some of these models of concurrency are primarily intended to support reasoning and specification, while others can be used through the entire development cycle, including design, implementation, proof, testing and simulation of concurrent systems. Some of these are based on <a href="/wiki/Message_passing" title="Message passing">message passing</a>, while others have different mechanisms for concurrency. </p><p>The proliferation of different models of concurrency has motivated some researchers to develop ways to unify these different theoretical models. For example, Lee and Sangiovanni-Vincentelli have demonstrated that a so-called "tagged-signal" model can be used to provide a common framework for defining the <a href="/wiki/Denotational_semantics" title="Denotational semantics">denotational semantics</a> of a variety of different models of concurrency,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> while Nielsen, Sassone, and Winskel have demonstrated that <a href="/wiki/Category_theory" title="Category theory">category theory</a> can be used to provide a similar unified understanding of different models.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The Concurrency Representation Theorem in the actor model provides a fairly general way to represent concurrent systems that are closed in the sense that they do not receive communications from outside. (Other concurrency systems, e.g., <a href="/wiki/Process_calculi" class="mw-redirect" title="Process calculi">process calculi</a> can be modeled in the actor model using a <a href="/wiki/Two-phase_commit_protocol" title="Two-phase commit protocol">two-phase commit protocol</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>) The mathematical denotation denoted by a closed system <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">S</span> is constructed increasingly better approximations from an initial behavior called <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">⊥<sub>S</sub></span> using a behavior approximating function <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced"><b>progression</b><sub>S</sub></span> to construct a denotation (meaning ) for <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">S</span> as follows:<sup id="cite_ref-clinger1981_14-0" class="reference"><a href="#cite_note-clinger1981-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced"><b>Denote</b><sub>S</sub> ≡ ⊔<sub>i∈ω</sub> <b>progression</b><sub>S</sub><sup>i</sup>(⊥<sub>S</sub>)</span></dd></dl></dd></dl> <p>In this way, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">S</span> can be mathematically characterized in terms of all its possible behaviors. </p> <div class="mw-heading mw-heading3"><h3 id="Logics">Logics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=5" title="Edit section: Logics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Various types of <a href="/wiki/Temporal_logic" title="Temporal logic">temporal logic</a><sup id="cite_ref-stirling_15-0" class="reference"><a href="#cite_note-stirling-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> can be used to help reason about concurrent systems. Some of these logics, such as <a href="/wiki/Linear_temporal_logic" title="Linear temporal logic">linear temporal logic</a> and <a href="/wiki/Computation_tree_logic" title="Computation tree logic">computation tree logic</a>, allow assertions to be made about the sequences of states that a concurrent system can pass through. Others, such as <a href="/w/index.php?title=Action_computational_tree_logic&action=edit&redlink=1" class="new" title="Action computational tree logic (page does not exist)">action computational tree logic</a>, <a href="/wiki/Hennessy%E2%80%93Milner_logic" title="Hennessy–Milner logic">Hennessy–Milner logic</a>, and <a href="/wiki/Leslie_Lamport" title="Leslie Lamport">Lamport's</a> <a href="/wiki/Temporal_logic_of_actions" title="Temporal logic of actions">temporal logic of actions</a>, build their assertions from sequences of <i>actions</i> (changes in state). The principal application of these logics is in writing specifications for concurrent systems.<sup id="cite_ref-cleaveland1996_7-1" class="reference"><a href="#cite_note-cleaveland1996-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Practice">Practice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=6" title="Edit section: Practice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Concurrency_(computer_science)" title="Special:EditPage/Concurrency (computer science)">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">April 2007</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><a href="/wiki/Concurrent_programming" class="mw-redirect" title="Concurrent programming">Concurrent programming</a> encompasses programming languages and algorithms used to implement concurrent systems. Concurrent programming is usually considered<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (August 2023)">by whom?</span></a></i>]</sup> to be more general than <a href="/wiki/Parallel_programming" class="mw-redirect" title="Parallel programming">parallel programming</a> because it can involve arbitrary and dynamic patterns of communication and interaction, whereas parallel systems generally<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (August 2023)">according to whom?</span></a></i>]</sup> have a predefined and well-structured communications pattern. The base goals of concurrent programming include <i>correctness</i>, <i>performance</i> and <i>robustness</i>. Concurrent systems such as <a href="/wiki/Operating_system" title="Operating system">Operating systems</a> and <a href="/wiki/Database_management_system" class="mw-redirect" title="Database management system">Database management systems</a> are generally designed<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (August 2023)">by whom?</span></a></i>]</sup> to operate indefinitely, including automatic recovery from failure, and not terminate unexpectedly (see <a href="/wiki/Concurrency_control" title="Concurrency control">Concurrency control</a>). Some<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:AUDIENCE" class="mw-redirect" title="Wikipedia:AUDIENCE"><span title="An editor has requested that an example be provided. (August 2023)">example needed</span></a></i>]</sup> concurrent systems implement a form of transparent concurrency, in which concurrent computational entities may compete for and share a single resource, but the complexities of this competition and sharing are shielded from the programmer. </p><p>Because they use shared resources, concurrent systems in general<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (August 2023)">according to whom?</span></a></i>]</sup> require the inclusion of some<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:AUDIENCE" class="mw-redirect" title="Wikipedia:AUDIENCE"><span title="An editor has requested that an example be provided. (August 2023)">example needed</span></a></i>]</sup> kind of <a href="/wiki/Arbiter_(electronics)" title="Arbiter (electronics)">arbiter</a> somewhere in their implementation (often in the underlying hardware), to control access to those resources. The use of arbiters introduces the possibility of <a href="/wiki/Indeterminacy_in_concurrent_computation" title="Indeterminacy in concurrent computation">indeterminacy in concurrent computation</a> which has major implications for practice including correctness and performance. For example, arbitration introduces <a href="/wiki/Unbounded_nondeterminism" title="Unbounded nondeterminism">unbounded nondeterminism</a> which raises issues with <a href="/wiki/Model_checking" title="Model checking">model checking</a> because it causes explosion in the state space and can even cause models to have an infinite number of states. </p><p>Some concurrent programming models include <a href="/wiki/Coprocess" title="Coprocess">coprocesses</a> and <a href="/wiki/Deterministic_concurrency" class="mw-redirect" title="Deterministic concurrency">deterministic concurrency</a>. In these models, threads of control explicitly <a href="/wiki/Yield_(multithreading)" title="Yield (multithreading)">yield</a> their timeslices, either to the system or to another process. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Dining_philosophers_problem" title="Dining philosophers problem">Dining philosophers problem</a></li> <li><a href="/wiki/Chu_space" title="Chu space">Chu space</a></li> <li><a href="/wiki/Client%E2%80%93server" class="mw-redirect" title="Client–server">Client–server</a> network nodes</li> <li><a href="/wiki/Clojure" title="Clojure">Clojure</a></li> <li><a href="/wiki/Cluster_computing" class="mw-redirect" title="Cluster computing">Cluster</a> nodes</li> <li><a href="/wiki/Concurrency_control" title="Concurrency control">Concurrency control</a></li> <li><a href="/wiki/Concurrent_computing" title="Concurrent computing">Concurrent computing</a></li> <li><a href="/wiki/Concurrent_object-oriented_programming" title="Concurrent object-oriented programming">Concurrent object-oriented programming</a></li> <li><a href="/wiki/Concurrency_pattern" title="Concurrency pattern">Concurrency pattern</a></li> <li><a href="/wiki/Construction_and_Analysis_of_Distributed_Processes" title="Construction and Analysis of Distributed Processes">Construction and Analysis of Distributed Processes</a> (CADP)</li> <li><a href="/wiki/D_(programming_language)" title="D (programming language)">D (programming language)</a></li> <li><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed system</a></li> <li><a href="/wiki/Elixir_(programming_language)" title="Elixir (programming language)">Elixir (programming language)</a></li> <li><a href="/wiki/Erlang_(programming_language)" title="Erlang (programming language)">Erlang (programming language)</a></li> <li><a href="/wiki/Go_(programming_language)" title="Go (programming language)">Go (programming language)</a></li> <li><a href="/wiki/Gordon_Pask" title="Gordon Pask">Gordon Pask</a></li> <li><a href="/wiki/International_Conference_on_Concurrency_Theory" title="International Conference on Concurrency Theory">International Conference on Concurrency Theory</a> (CONCUR)</li> <li><a href="/wiki/OpenMP" title="OpenMP">OpenMP</a></li> <li><a href="/wiki/Parallel_computing" title="Parallel computing">Parallel computing</a></li> <li><a href="/wiki/Partitioned_global_address_space" title="Partitioned global address space">Partitioned global address space</a></li> <li><a href="/wiki/Process_(computing)" title="Process (computing)">Processes</a></li> <li><a href="/wiki/Ptolemy_Project" title="Ptolemy Project">Ptolemy Project</a></li> <li><a href="/wiki/Rust_(programming_language)" title="Rust (programming language)">Rust (programming language)</a></li> <li><a href="/wiki/Sheaf_(mathematics)" title="Sheaf (mathematics)">Sheaf (mathematics)</a></li> <li><a href="/wiki/Thread_(computing)" title="Thread (computing)">Threads</a></li> <li><a href="/wiki/X10_(programming_language)" title="X10 (programming language)">X10 (programming language)</a></li> <li><a href="/wiki/Structured_concurrency" title="Structured concurrency">Structured concurrency</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1"><i>Operating System Concepts</i>. Wiley. 29 July 2008. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0470128725" title="Special:BookSources/978-0470128725"><bdi>978-0470128725</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Operating+System+Concepts&rft.pub=Wiley&rft.date=2008-07-29&rft.isbn=978-0470128725&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Computer Organization and Design: The Hardware/Software Interface</i>. The Morgan Kaufmann Series in Computer Architecture and Design. Morgan Kaufmann. 2012. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0123747501" title="Special:BookSources/978-0123747501"><bdi>978-0123747501</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+Organization+and+Design%3A+The+Hardware%2FSoftware+Interface&rft.series=The+Morgan+Kaufmann+Series+in+Computer+Architecture+and+Design&rft.pub=Morgan+Kaufmann&rft.date=2012&rft.isbn=978-0123747501&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-:2-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Distributed Systems: Concepts and Design</i>. Pearson. 2012. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0132143011" title="Special:BookSources/978-0132143011"><bdi>978-0132143011</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Distributed+Systems%3A+Concepts+and+Design&rft.pub=Pearson&rft.date=2012&rft.isbn=978-0132143011&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-:3-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFQuinn1994" class="citation book cs1">Quinn, Michael Jay (1994). <i>Parallel Computing: Theory and Practice</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0070512948" title="Special:BookSources/978-0070512948"><bdi>978-0070512948</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Parallel+Computing%3A+Theory+and+Practice&rft.pub=McGraw-Hill&rft.date=1994&rft.isbn=978-0070512948&rft.aulast=Quinn&rft.aufirst=Michael+Jay&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-:4-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Parallel and Distributed Computing Handbook</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0070730205" title="Special:BookSources/978-0070730205"><bdi>978-0070730205</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Parallel+and+Distributed+Computing+Handbook&rft.isbn=978-0070730205&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Parallel and Concurrent Programming in Haskell</i>. O'Reilly Media. 2013. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781449335922" title="Special:BookSources/9781449335922"><bdi>9781449335922</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Parallel+and+Concurrent+Programming+in+Haskell&rft.pub=O%27Reilly+Media&rft.date=2013&rft.isbn=9781449335922&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-cleaveland1996-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-cleaveland1996_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-cleaveland1996_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCleavelandScott_Smolka1996" class="citation journal cs1">Cleaveland, Rance; Scott Smolka (December 1996). <a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F242223.242252">"Strategic Directions in Concurrency Research"</a>. <i>ACM Computing Surveys</i>. <b>28</b> (4): 607. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F242223.242252">10.1145/242223.242252</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13264261">13264261</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Computing+Surveys&rft.atitle=Strategic+Directions+in+Concurrency+Research&rft.volume=28&rft.issue=4&rft.pages=607&rft.date=1996-12&rft_id=info%3Adoi%2F10.1145%2F242223.242252&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A13264261%23id-name%3DS2CID&rft.aulast=Cleaveland&rft.aufirst=Rance&rft.au=Scott+Smolka&rft_id=https%3A%2F%2Fdoi.org%2F10.1145%252F242223.242252&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCampbellJohnsonMillerToub2010" class="citation book cs1">Campbell, Colin; Johnson, Ralph; Miller, Ade; Toub, Stephen (August 2010). <a rel="nofollow" class="external text" href="http://msdn.microsoft.com/en-us/library/ff963542.aspx"><i>Parallel Programming with Microsoft .NET</i></a>. Microsoft Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7356-5159-3" title="Special:BookSources/978-0-7356-5159-3"><bdi>978-0-7356-5159-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Parallel+Programming+with+Microsoft+.NET&rft.pub=Microsoft+Press&rft.date=2010-08&rft.isbn=978-0-7356-5159-3&rft.aulast=Campbell&rft.aufirst=Colin&rft.au=Johnson%2C+Ralph&rft.au=Miller%2C+Ade&rft.au=Toub%2C+Stephen&rft_id=http%3A%2F%2Fmsdn.microsoft.com%2Fen-us%2Flibrary%2Fff963542.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFilmanDaniel_Friedman1984" class="citation book cs1">Filman, Robert; Daniel Friedman (1984). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/coordinatedcompu0000film"><i>Coordinated Computing - Tools and Techniques for Distributed Software</i></a></span>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-022439-1" title="Special:BookSources/978-0-07-022439-1"><bdi>978-0-07-022439-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Coordinated+Computing+-+Tools+and+Techniques+for+Distributed+Software&rft.pub=McGraw-Hill&rft.date=1984&rft.isbn=978-0-07-022439-1&rft.aulast=Filman&rft.aufirst=Robert&rft.au=Daniel+Friedman&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcoordinatedcompu0000film&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKellerChristoph_KeßlerJesper_Träff2001" class="citation book cs1">Keller, Jörg; Christoph Keßler; Jesper Träff (2001). <i>Practical PRAM Programming</i>. John Wiley and Sons.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Practical+PRAM+Programming&rft.pub=John+Wiley+and+Sons&rft.date=2001&rft.aulast=Keller&rft.aufirst=J%C3%B6rg&rft.au=Christoph+Ke%C3%9Fler&rft.au=Jesper+Tr%C3%A4ff&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeeAlberto_Sangiovanni-Vincentelli1998" class="citation journal cs1">Lee, Edward; Alberto Sangiovanni-Vincentelli (December 1998). <a rel="nofollow" class="external text" href="http://ptolemy.eecs.berkeley.edu/publications/papers/98/framework/ieeeVersion.pdf">"A Framework for Comparing Models of Computation"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/IEEE_Transactions_on_CAD" class="mw-redirect" title="IEEE Transactions on CAD">IEEE Transactions on CAD</a></i>. <b>17</b> (12): 1217–1229. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F43.736561">10.1109/43.736561</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+CAD&rft.atitle=A+Framework+for+Comparing+Models+of+Computation&rft.volume=17&rft.issue=12&rft.pages=1217-1229&rft.date=1998-12&rft_id=info%3Adoi%2F10.1109%2F43.736561&rft.aulast=Lee&rft.aufirst=Edward&rft.au=Alberto+Sangiovanni-Vincentelli&rft_id=http%3A%2F%2Fptolemy.eecs.berkeley.edu%2Fpublications%2Fpapers%2F98%2Fframework%2FieeeVersion.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMogens_NielsenVladimiro_SassoneGlynn_Winskel1993" class="citation conference cs1">Mogens Nielsen; Vladimiro Sassone; Glynn Winskel (1993). <a rel="nofollow" class="external text" href="http://citeseer.ist.psu.edu/article/nielsen94relationships.html">"Relationships Between Models of Concurrency"</a>. <i>REX School/Symposium</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Relationships+Between+Models+of+Concurrency&rft.btitle=REX+School%2FSymposium&rft.date=1993&rft.au=Mogens+Nielsen&rft.au=Vladimiro+Sassone&rft.au=Glynn+Winskel&rft_id=http%3A%2F%2Fciteseer.ist.psu.edu%2Farticle%2Fnielsen94relationships.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Frederick Knabe. A Distributed Protocol for Channel-Based Communication with Choice PARLE 1992.</span> </li> <li id="cite_note-clinger1981-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-clinger1981_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliam_Clinger1981" class="citation journal cs1"><a href="/wiki/William_Clinger_(computer_scientist)" title="William Clinger (computer scientist)">William Clinger</a> (June 1981). "Foundations of Actor Semantics". Mathematics Doctoral Dissertation. MIT. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F6935">1721.1/6935</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Foundations+of+Actor+Semantics&rft.date=1981-06&rft_id=info%3Ahdl%2F1721.1%2F6935&rft.au=William+Clinger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-stirling-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-stirling_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoscoe2001" class="citation book cs1">Roscoe, Colin (2001). <i>Modal and Temporal Properties of Processes</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-98717-0" title="Special:BookSources/978-0-387-98717-0"><bdi>978-0-387-98717-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modal+and+Temporal+Properties+of+Processes&rft.pub=Springer&rft.date=2001&rft.isbn=978-0-387-98717-0&rft.aulast=Roscoe&rft.aufirst=Colin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLynch1996" class="citation book cs1">Lynch, Nancy A. (1996). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/distributedalgor0000lync"><i>Distributed Algorithms</i></a></span>. Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-55860-348-6" title="Special:BookSources/978-1-55860-348-6"><bdi>978-1-55860-348-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Distributed+Algorithms&rft.pub=Morgan+Kaufmann&rft.date=1996&rft.isbn=978-1-55860-348-6&rft.aulast=Lynch&rft.aufirst=Nancy+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdistributedalgor0000lync&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTanenbaumVan_Steen2002" class="citation book cs1">Tanenbaum, Andrew S.; Van Steen, Maarten (2002). <i>Distributed Systems: Principles and Paradigms</i>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-088893-8" title="Special:BookSources/978-0-13-088893-8"><bdi>978-0-13-088893-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Distributed+Systems%3A+Principles+and+Paradigms&rft.pub=Prentice+Hall&rft.date=2002&rft.isbn=978-0-13-088893-8&rft.aulast=Tanenbaum&rft.aufirst=Andrew+S.&rft.au=Van+Steen%2C+Maarten&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKurki-Suonio2005" class="citation book cs1">Kurki-Suonio, Reino (2005). <i>A Practical Theory of Reactive Systems</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-23342-8" title="Special:BookSources/978-3-540-23342-8"><bdi>978-3-540-23342-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Practical+Theory+of+Reactive+Systems&rft.pub=Springer&rft.date=2005&rft.isbn=978-3-540-23342-8&rft.aulast=Kurki-Suonio&rft.aufirst=Reino&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarg2002" class="citation book cs1">Garg, Vijay K. (2002). <i>Elements of Distributed Computing</i>. Wiley-IEEE Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-03600-5" title="Special:BookSources/978-0-471-03600-5"><bdi>978-0-471-03600-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elements+of+Distributed+Computing&rft.pub=Wiley-IEEE+Press&rft.date=2002&rft.isbn=978-0-471-03600-5&rft.aulast=Garg&rft.aufirst=Vijay+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMageeKramer,_Jeff2006" class="citation book cs1">Magee, Jeff; Kramer, Jeff (2006). <i>Concurrency: State Models and Java Programming</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-09355-9" title="Special:BookSources/978-0-470-09355-9"><bdi>978-0-470-09355-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Concurrency%3A+State+Models+and+Java+Programming&rft.pub=Wiley&rft.date=2006&rft.isbn=978-0-470-09355-9&rft.aulast=Magee&rft.aufirst=Jeff&rft.au=Kramer%2C+Jeff&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConcurrency+%28computer+science%29" class="Z3988"></span></li> <li>Distefano, S., & Bruneo, D. (2015). <i>Quantitative assessments of distributed systems: Methodologies and techniques</i> (1st ed.). Somerset: John Wiley & Sons Inc.<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781119131144" title="Special:BookSources/9781119131144">9781119131144</a></li> <li>Bhattacharyya, S. S. (2013;2014;). <i>Handbook of signal processing systems</i> (Second;2;2nd 2013; ed.). New York, NY: Springer.10.1007/978-1-4614-6859-2 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781461468592" title="Special:BookSources/9781461468592">9781461468592</a></li> <li>Wolter, K. (2012;2014;). <i>Resilience assessment and evaluation of computing systems</i> (1. Aufl.;1; ed.). London;Berlin;: Springer. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783642290329" title="Special:BookSources/9783642290329">9783642290329</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Concurrency_(computer_science)&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://processalgebra.blogspot.com/">Process Algebra Diary - Prof. Luca Aceto's blog on Concurrency Theory</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060128114620/http://vl.fmnet.info/concurrent/">Concurrent Systems</a> at <a rel="nofollow" class="external text" href="http://vlib.org/">The WWW Virtual Library</a></li> <li><a rel="nofollow" class="external text" href="http://shairosenfeld.com/concurrency.html">Concurrency patterns presentation</a> given at <a rel="nofollow" class="external text" href="http://scaleconf.org">scaleconf</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist 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aria-labelledby="Concurrent_computing" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini 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href="/wiki/Indeterminacy_in_concurrent_computation" title="Indeterminacy in concurrent computation">Indeterminacy</a></li> <li><a href="/wiki/Linearizability" title="Linearizability">Linearizability</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Process_calculus" title="Process calculus">Process calculi</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Communicating_sequential_processes" title="Communicating sequential processes">CSP</a></li> <li><a href="/wiki/Calculus_of_communicating_systems" title="Calculus of communicating systems">CCS</a></li> <li><a href="/wiki/Algebra_of_Communicating_Processes" class="mw-redirect" title="Algebra of Communicating Processes">ACP</a></li> <li><a href="/wiki/Language_Of_Temporal_Ordering_Specification" class="mw-redirect" title="Language Of Temporal Ordering Specification">LOTOS</a></li> 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