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id="toc-Initial_problem_and_solution_overview-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theoretical_implementation_of_bit-string_signatures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theoretical_implementation_of_bit-string_signatures"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Theoretical implementation of bit-string signatures</span> </div> </a> <ul id="toc-Theoretical_implementation_of_bit-string_signatures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pseudocode_for_bit-string_signatures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pseudocode_for_bit-string_signatures"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Pseudocode for bit-string signatures</span> </div> </a> <ul id="toc-Pseudocode_for_bit-string_signatures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" 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.mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"WorkBench" redirects here. For other uses, see <a href="/wiki/Workbench_(disambiguation)" class="mw-disambig" title="Workbench (disambiguation)">Workbench (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vevent"><caption class="infobox-title summary">BitFunnel</caption><tbody><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Programmer" title="Programmer">Developer(s)</a></th><td class="infobox-data"><a href="/wiki/Microsoft" title="Microsoft">Microsoft</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Initial release</th><td class="infobox-data">2016<span class="noprint">; 8 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">2016</span>)</span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Repository_(version_control)" title="Repository (version control)">Repository</a></th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://github.com/BitFunnel">github<wbr />.com<wbr />/BitFunnel</a></span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Written in</th><td class="infobox-data"><a href="/wiki/C%2B%2B" title="C++">C++</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Computing_platform" title="Computing platform">Platform</a></th><td class="infobox-data"><a href="/wiki/Microsoft_Windows" title="Microsoft Windows">Windows</a>, <a href="/wiki/MacOS" title="MacOS">macOS</a>, <a href="/wiki/Ubuntu" title="Ubuntu">Ubuntu</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_categories#Categorization_approaches" title="Software categories">Type</a></th><td class="infobox-data"><a href="/wiki/Search_engine_indexing" title="Search engine indexing">Search engine indexing</a> algorithm</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="/wiki/MIT_License" title="MIT License">MIT License</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="http://bitfunnel.org/">bitfunnel<wbr />.org</a></span></td></tr></tbody></table> <p><b>BitFunnel</b> is the <a href="/wiki/Search_engine_indexing" title="Search engine indexing">search engine indexing</a> algorithm and a set of components used in the <a href="/wiki/Bing_(search_engine)" class="mw-redirect" title="Bing (search engine)">Bing search engine</a>,<sup id="cite_ref-InfoWorld_1-0" class="reference"><a href="#cite_note-InfoWorld-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> which were made open source in 2016.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> BitFunnel uses bit-sliced signatures instead of an <a href="/wiki/Inverted_index" title="Inverted index">inverted index</a> in an attempt to reduce operations cost.<sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Progress on the implementation of BitFunnel was made public in early 2016, with the expectation that there would be a usable implementation later that year.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In September 2016, the source code was made available via <a href="/wiki/GitHub" title="GitHub">GitHub</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> A paper discussing the BitFunnel algorithm and implementation was released as through the <a href="/wiki/Special_Interest_Group_on_Information_Retrieval" title="Special Interest Group on Information Retrieval">Special Interest Group on Information Retrieval</a> of the <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a> in 2017 and won the Best Paper Award.<sup id="cite_ref-:0_3-1" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><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> </p> <div class="mw-heading mw-heading2"><h2 id="Components">Components</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=2" title="Edit section: Components"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>BitFunnel consists of three major components:<sup id="cite_ref-InfoWorld_1-1" class="reference"><a href="#cite_note-InfoWorld-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <ul><li>BitFunnel – the text search/retrieval system itself</li> <li>WorkBench – a tool for preparing text for use in BitFunnel</li> <li>NativeJIT – a software component that takes expressions that use <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> <a href="/wiki/Data_structure" title="Data structure">data structures</a> and transforms them into highly optimized <a href="/wiki/Assembly_code" class="mw-redirect" title="Assembly code">assembly code</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=3" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Initial_problem_and_solution_overview">Initial problem and solution overview</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=4" title="Edit section: Initial problem and solution overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The BitFunnel paper describes the "matching problem", which occurs when an algorithm must identify documents through the usage of keywords. The goal of the problem is to identify a set of matches given a corpus to search and a query of keyword terms to match against. This problem is commonly solved through <a href="/wiki/Inverted_index" title="Inverted index">inverted indexes</a>, where each searchable item is maintained with a <a href="/wiki/Map_(computer_science)" class="mw-redirect" title="Map (computer science)">map</a> of keywords.<sup id="cite_ref-:0_3-2" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In contrast, BitFunnel represents each searchable item through a signature. A signature is a sequence of bits which describe a <a href="/wiki/Bloom_filter" title="Bloom filter">Bloom filter</a> of the searchable terms in a given searchable item. The bloom filter is constructed through hashing through several bit positions.<sup id="cite_ref-:0_3-3" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Theoretical_implementation_of_bit-string_signatures">Theoretical implementation of bit-string signatures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=5" title="Edit section: Theoretical implementation of bit-string signatures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The signature of a document (D) can be described as the logical-or of its term signatures: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {S_{D}}}=\bigcup _{t\in D}{\overrightarrow {S_{t}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>=</mo> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>∈</mo> <mi>D</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {S_{D}}}=\bigcup _{t\in D}{\overrightarrow {S_{t}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/747df723f085f7d6a09adf1cb7f5d9b80d25bf65" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; margin-top: -0.398ex; width:12.008ex; height:6.676ex;" alt="{\displaystyle {\overrightarrow {S_{D}}}=\bigcup _{t\in D}{\overrightarrow {S_{t}}}}"></span> </p><p>Similarly, a query for a document (Q) can be defined as a union: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {S_{Q}}}=\bigcup _{t\in Q}{\overrightarrow {S_{t}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>=</mo> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>∈</mo> <mi>Q</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {S_{Q}}}=\bigcup _{t\in Q}{\overrightarrow {S_{t}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aca08c0f9f8b112d5de3a0cfb4095b7459da6aac" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; margin-top: -0.398ex; width:11.886ex; height:6.843ex;" alt="{\displaystyle {\overrightarrow {S_{Q}}}=\bigcup _{t\in Q}{\overrightarrow {S_{t}}}}"></span> </p><p>Additionally, a document D is a member of the set <i>M'</i> when the following condition is satisfied: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a9517083916189ea4991669e0a77b16d6197c8b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-top: -0.398ex; width:15.003ex; height:4.509ex;" alt="{\displaystyle {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}}"></span> </p><p>This knowledge is then combined to produce a formula where <i>M'</i> is identified by documents which match the query signature: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M'=\left\{D\in C\mid {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}\right\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>M</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mi>D</mi> <mo>∈</mo> <mi>C</mi> <mo>∣</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M'=\left\{D\in C\mid {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}\right\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfb4a5814b94d8e5895cbe4b63a008e91259990e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.24ex; height:6.176ex;" alt="{\displaystyle M'=\left\{D\in C\mid {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}\right\}}"></span> </p><p>These steps and their proofs are discussed in the 2017 paper.<sup id="cite_ref-:0_3-4" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pseudocode_for_bit-string_signatures">Pseudocode for bit-string signatures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=BitFunnel&action=edit&section=6" title="Edit section: Pseudocode for bit-string signatures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This algorithm is described in the 2017 paper.<sup id="cite_ref-:0_3-5" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}M'=\emptyset \\{\texttt {foreach}}\ D\in C\ {\texttt {do}}\\\qquad {\texttt {if}}\ {\overrightarrow {S_{D}}}\cap {\overrightarrow {S_{Q}}}={\overrightarrow {S_{Q}}}\ {\texttt {then}}\\\qquad \qquad M'=M'\cup \{D\}\\\qquad {\texttt {endif}}\\{\texttt {endfor}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mi>M</mi> <mo>′</mo> </msup> <mo>=</mo> <mi mathvariant="normal">∅</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">foreach</mtext> </mrow> </mrow> <mtext> </mtext> <mi>D</mi> <mo>∈</mo> <mi>C</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">do</mtext> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">if</mtext> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>→</mo> </mover> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">then</mtext> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mspace width="2em" /> <mspace width="2em" /> <msup> <mi>M</mi> <mo>′</mo> </msup> <mo>=</mo> <msup> <mi>M</mi> <mo>′</mo> </msup> <mo>∪</mo> <mo fence="false" stretchy="false">{</mo> <mi>D</mi> <mo fence="false" stretchy="false">}</mo> </mtd> </mtr> <mtr> <mtd> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">endif</mtext> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="monospace">endfor</mtext> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}M'=\emptyset \\{\texttt {foreach}}\ D\in C\ {\texttt {do}}\\\qquad {\texttt {if}}\ {\overrightarrow {S_{D}}}\cap {\overrightarrow {S_{Q}}}={\overrightarrow {S_{Q}}}\ {\texttt {then}}\\\qquad \qquad M'=M'\cup \{D\}\\\qquad {\texttt {endif}}\\{\texttt {endfor}}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac32d2d5ab5b2d938420c18955bca05a90b2b99a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.838ex; width:28.884ex; height:20.676ex;" alt="{\displaystyle {\begin{array}{l}M'=\emptyset \\{\texttt {foreach}}\ D\in C\ {\texttt {do}}\\\qquad {\texttt {if}}\ {\overrightarrow {S_{D}}}\cap {\overrightarrow {S_{Q}}}={\overrightarrow {S_{Q}}}\ {\texttt {then}}\\\qquad \qquad M'=M'\cup \{D\}\\\qquad {\texttt {endif}}\\{\texttt {endfor}}\end{array}}}"></span> </p> <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=BitFunnel&action=edit&section=7" 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"><ol class="references"> <li id="cite_note-InfoWorld-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-InfoWorld_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-InfoWorld_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 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Retrieved <span class="nowrap">2020-06-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=bitfunnel.org&rft.atitle=When+will+BitFunnel+be+usable%3F+%C2%B7+BitFunnel&rft_id=http%3A%2F%2Fbitfunnel.org%2Fprogress%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABitFunnel" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://github.com/BitFunnel/BitFunnel"><i>BitFunnel/BitFunnel</i></a>, BitFunnel, 2020-05-12<span class="reference-accessdate">, retrieved <span class="nowrap">2020-06-12</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=BitFunnel%2FBitFunnel&rft.pub=BitFunnel&rft.date=2020-05-12&rft_id=https%3A%2F%2Fgithub.com%2FBitFunnel%2FBitFunnel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABitFunnel" 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 web cs1"><a rel="nofollow" class="external text" href="https://sigir.org/awards/best-paper-awards/">"SIGIR Best Paper Awards"</a>. ACM<span class="reference-accessdate">. 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open-source software">free and open-source software (FOSS)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Overview</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_and_open_source" title="Microsoft and open source">Microsoft and open source</a></li> <li><a href="/wiki/Shared_Source_Initiative" title="Shared Source Initiative">Shared Source Initiative</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Applications</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/3D_Movie_Maker" title="3D Movie Maker">3D Movie Maker</a></li> <li><a href="/wiki/Atom_(text_editor)" title="Atom (text editor)">Atom</a></li> <li><a href="/wiki/Conference_XP" title="Conference XP">Conference XP</a></li> <li><a href="/wiki/Family.Show" title="Family.Show">Family.Show</a></li> <li><a href="/wiki/File_Manager_(Windows)" class="mw-redirect" title="File Manager (Windows)">File Manager</a></li> <li><a href="/wiki/Open_Live_Writer" title="Open Live Writer">Open Live Writer</a></li> <li><a href="/wiki/Microsoft_PowerToys" title="Microsoft PowerToys">Microsoft PowerToys</a></li> <li><a href="/wiki/Windows_Terminal" title="Windows Terminal">Terminal</a></li> <li><a href="/wiki/Windows_Calculator" title="Windows Calculator">Windows Calculator</a></li> <li><a href="/wiki/Windows_Console" title="Windows Console">Windows Console</a></li> <li><a href="/wiki/Windows_Package_Manager" title="Windows Package Manager">Windows Package Manager</a></li> <li><a href="/wiki/WorldWide_Telescope" title="WorldWide Telescope">WorldWide Telescope</a></li> <li><a href="/wiki/XML_Notepad" title="XML Notepad">XML Notepad</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Video games</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Allegiance_(video_game)" title="Allegiance (video game)">Allegiance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Programming<br />languages</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/Bosque_(programming_language)" title="Bosque (programming language)">Bosque</a></li> <li><a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a></li> <li><a href="/wiki/Dafny" title="Dafny">Dafny</a></li> <li><a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a></li> <li><a href="/wiki/F*_(programming_language)" title="F* (programming language)">F*</a></li> <li><a href="/wiki/GW-BASIC" title="GW-BASIC">GW-BASIC</a></li> <li><a href="/wiki/IronPython" title="IronPython">IronPython</a></li> <li><a href="/wiki/IronRuby" title="IronRuby">IronRuby</a></li> <li><a href="/wiki/Lean_(proof_assistant)" title="Lean (proof assistant)">Lean</a></li> <li><a href="/wiki/P_(programming_language)" title="P (programming language)">P</a></li> <li><a href="/wiki/Microsoft_Power_Fx" title="Microsoft Power Fx">Power Fx</a></li> <li><a href="/wiki/PowerShell" title="PowerShell">PowerShell</a></li> <li><a href="/wiki/Project_Verona" title="Project Verona">Project Verona</a></li> <li><a href="/wiki/Q_Sharp" title="Q Sharp">Q#</a></li> <li><a href="/wiki/Microsoft_Small_Basic" title="Microsoft Small Basic">Small Basic Online</a></li> <li><a href="/wiki/TypeScript" title="TypeScript">TypeScript</a></li> <li><a href="/wiki/Visual_Basic_.NET" class="mw-redirect" title="Visual Basic .NET">Visual Basic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Frameworks,<br />development tools</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/.NET" title=".NET">.NET</a></li> <li><a href="/wiki/.NET_Framework" title=".NET Framework">.NET Framework</a></li> <li><a href="/wiki/.NET_Gadgeteer" title=".NET Gadgeteer">.NET Gadgeteer</a></li> <li><a href="/wiki/.NET_MAUI" class="mw-redirect" title=".NET MAUI">.NET MAUI</a></li> <li><a href="/wiki/.NET_Micro_Framework" title=".NET Micro Framework">.NET Micro Framework</a></li> <li><a href="/wiki/AirSim" title="AirSim">AirSim</a></li> <li><a href="/wiki/ASP.NET" title="ASP.NET">ASP.NET</a></li> <li><a href="/wiki/ASP.NET_AJAX" title="ASP.NET AJAX">ASP.NET AJAX</a></li> <li><a href="/wiki/ASP.NET_Core" title="ASP.NET Core">ASP.NET Core</a></li> <li><a href="/wiki/ASP.NET_MVC" title="ASP.NET MVC">ASP.NET MVC</a></li> <li><a href="/wiki/ASP.NET_Razor" title="ASP.NET Razor">ASP.NET Razor</a></li> <li><a href="/wiki/ASP.NET_Web_Forms" title="ASP.NET Web Forms">ASP.NET Web Forms</a></li> <li><a href="/wiki/Avalonia_(software_framework)" title="Avalonia (software framework)">Avalonia</a></li> <li><a href="/wiki/Babylon.js" title="Babylon.js">Babylon.js</a></li> <li><a class="mw-selflink selflink">BitFunnel</a></li> <li><a href="/wiki/Blazor" title="Blazor">Blazor</a></li> <li><a href="/wiki/C%2B%2B/WinRT" title="C++/WinRT">C++/WinRT</a></li> <li><a href="/wiki/Confidential_Consortium_Framework" title="Confidential Consortium Framework">CCF</a></li> <li><a href="/wiki/Chakra_(JavaScript_engine)" title="Chakra (JavaScript engine)">ChakraCore</a></li> <li><a href="/wiki/CLR_Profiler" title="CLR Profiler">CLR Profiler</a></li> <li><a href="/wiki/Dapr" title="Dapr">Dapr</a></li> <li><a href="/wiki/DeepSpeed" title="DeepSpeed">DeepSpeed</a></li> <li><a href="/wiki/DiskSpd" title="DiskSpd">DiskSpd</a></li> <li><a href="/wiki/Dryad_(programming)" title="Dryad (programming)">Dryad</a></li> <li><a href="/wiki/Dynamic_Language_Runtime" title="Dynamic Language Runtime">Dynamic Language Runtime</a></li> <li><a href="/wiki/EBPF_on_Windows" class="mw-redirect" title="EBPF on Windows">eBPF on Windows</a></li> <li><a href="/wiki/Electron_(software_framework)" title="Electron (software framework)">Electron</a></li> <li><a href="/wiki/Entity_Framework" title="Entity Framework">Entity Framework</a></li> <li><a href="/wiki/Fluent_Design_System" title="Fluent Design System">Fluent Design System</a></li> <li><a href="/wiki/Fluid_Framework" title="Fluid Framework">Fluid Framework</a></li> <li><a href="/wiki/Infer.NET" title="Infer.NET">Infer.NET</a></li> <li><a href="/wiki/LightGBM" title="LightGBM">LightGBM</a></li> <li><a href="/wiki/Managed_Extensibility_Framework" title="Managed Extensibility Framework">Managed Extensibility Framework</a></li> <li><a href="/wiki/Microsoft_Automatic_Graph_Layout" title="Microsoft Automatic Graph Layout">Microsoft Automatic Graph Layout</a></li> <li><a href="/wiki/Microsoft_C%2B%2B_Standard_Library" class="mw-redirect" title="Microsoft C++ Standard Library">Microsoft C++ Standard Library</a></li> <li><a href="/wiki/Microsoft_Cognitive_Toolkit" title="Microsoft Cognitive Toolkit">Microsoft Cognitive Toolkit</a></li> <li><a href="/wiki/Metro_(design_language)" title="Metro (design language)">Microsoft Design Language</a></li> <li><a href="/wiki/Microsoft_Detours" title="Microsoft Detours">Microsoft Detours</a></li> <li><a href="/wiki/Microsoft_Enterprise_Library" title="Microsoft Enterprise Library">Microsoft Enterprise Library</a></li> <li><a href="/wiki/Microsoft_SEAL" title="Microsoft SEAL">Microsoft SEAL</a></li> <li><a href="/wiki/Mimalloc" title="Mimalloc">mimalloc</a></li> <li><a href="/wiki/Mixed_Reality_Toolkit" title="Mixed Reality Toolkit">Mixed Reality Toolkit</a></li> <li><a href="/wiki/ML.NET" title="ML.NET">ML.NET</a></li> <li><a href="/wiki/Mod_mono" title="Mod mono">mod_mono</a></li> <li><a href="/wiki/Mono_(software)" title="Mono (software)">Mono</a></li> <li><a href="/wiki/MonoDevelop" title="MonoDevelop">MonoDevelop</a></li> <li><a href="/wiki/MSBuild" title="MSBuild">MSBuild</a></li> <li><a href="/wiki/MsQuic" title="MsQuic">MsQuic</a></li> <li><a href="/wiki/Neural_Network_Intelligence" title="Neural Network Intelligence">Neural Network Intelligence</a></li> <li><a href="/wiki/Npm" title="Npm">npm</a></li> <li><a href="/wiki/NuGet" title="NuGet">NuGet</a></li> <li><a href="/wiki/OneFuzz" title="OneFuzz">OneFuzz</a></li> <li><a href="/wiki/Open_Management_Infrastructure" title="Open Management Infrastructure">Open Management Infrastructure</a></li> <li><a href="/wiki/Open_Neural_Network_Exchange" title="Open Neural Network Exchange">Open Neural Network Exchange</a></li> <li><a href="/wiki/Open_Service_Mesh" title="Open Service Mesh">Open Service Mesh</a></li> <li><a href="/wiki/Open_XML_SDK" class="mw-redirect" title="Open XML SDK">Open XML SDK</a></li> <li><a href="/wiki/Orleans_(software_framework)" title="Orleans (software framework)">Orleans</a></li> <li><a href="/wiki/Playwright_(software)" title="Playwright (software)">Playwright</a></li> <li><a href="/wiki/ProcDump" title="ProcDump">ProcDump</a></li> <li><a href="/wiki/Process_Monitor" title="Process Monitor">ProcMon</a></li> <li><a href="/wiki/Python_Tools_for_Visual_Studio" title="Python Tools for Visual Studio">Python Tools for Visual Studio</a></li> <li><a href="/wiki/R_Tools_for_Visual_Studio" title="R Tools for Visual Studio">R Tools for Visual Studio</a></li> <li><a href="/wiki/RecursiveExtractor" class="mw-redirect" title="RecursiveExtractor">RecursiveExtractor</a></li> <li><a href="/wiki/Roslyn_(compiler)" title="Roslyn (compiler)">Roslyn</a></li> <li><a href="/wiki/Sandcastle_(software)" title="Sandcastle (software)">Sandcastle</a></li> <li><a href="/wiki/SignalR" title="SignalR">SignalR</a></li> <li><a href="/wiki/StyleCop" title="StyleCop">StyleCop</a></li> <li><a href="/wiki/SVNBridge" title="SVNBridge">SVNBridge</a></li> <li><a href="/wiki/T2_Temporal_Prover" title="T2 Temporal Prover">T2 Temporal Prover</a></li> <li><a href="/wiki/Text_Template_Transformation_Toolkit" title="Text Template Transformation Toolkit">Text Template Transformation Toolkit</a></li> <li><a href="/wiki/TLA%2B_Toolbox" class="mw-redirect" title="TLA+ Toolbox">TLA+ Toolbox</a></li> <li><a href="/wiki/U-Prove" title="U-Prove">U-Prove</a></li> <li><a href="/wiki/Vcpkg" title="Vcpkg">vcpkg</a></li> <li><a href="/wiki/Virtual_File_System_for_Git" title="Virtual File System for Git">Virtual File System for Git</a></li> <li><a href="/wiki/Voldemort_(distributed_data_store)" title="Voldemort (distributed data store)">Voldemort</a></li> <li><a href="/wiki/VoTT" title="VoTT">VoTT</a></li> <li><a href="/wiki/Vowpal_Wabbit" title="Vowpal Wabbit">Vowpal Wabbit</a></li> <li><a href="/wiki/Windows_App_SDK" title="Windows App SDK">Windows App SDK</a></li> <li><a href="/wiki/Windows_Communication_Foundation" title="Windows Communication Foundation">Windows Communication Foundation</a></li> <li><a href="/wiki/Windows_Driver_Frameworks" title="Windows Driver Frameworks">Windows Driver Frameworks</a> <ul><li><a href="/wiki/Kernel-Mode_Driver_Framework" title="Kernel-Mode Driver Framework">KMDF</a></li> <li><a href="/wiki/User-Mode_Driver_Framework" title="User-Mode Driver Framework">UMDF</a></li></ul></li> <li><a href="/wiki/Windows_Forms" title="Windows Forms">Windows Forms</a></li> <li><a href="/wiki/Windows_Presentation_Foundation" title="Windows Presentation Foundation">Windows Presentation Foundation</a></li> <li><a href="/wiki/Windows_Template_Library" title="Windows Template Library">Windows Template Library</a></li> <li><a href="/wiki/Windows_UI_Library" title="Windows UI Library">Windows UI Library</a></li> <li><a href="/wiki/WinJS" title="WinJS">WinJS</a></li> <li><a href="/wiki/WinObjC" class="mw-redirect" title="WinObjC">WinObjC</a></li> <li><a href="/wiki/WiX" title="WiX">WiX</a></li> <li><a href="/wiki/XDP_for_Windows" class="mw-redirect" title="XDP for Windows">XDP for Windows</a></li> <li><a href="/wiki/XSP_(software)" title="XSP (software)">XSP</a></li> <li><a href="/wiki/XUnit.net" title="XUnit.net">xUnit.net</a></li> <li><a href="/wiki/Z3_Theorem_Prover" title="Z3 Theorem Prover">Z3 Theorem Prover</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Operating systems</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/MS-DOS" title="MS-DOS">MS-DOS</a> (v1.25, v2.0 & v4.0)</li> <li><a href="/wiki/Barrelfish_(operating_system)" title="Barrelfish (operating system)">Barrelfish</a></li> <li><a href="/wiki/SONiC_(operating_system)" title="SONiC (operating system)">SONiC</a></li> <li><a href="/wiki/Azure_Linux" title="Azure Linux">Azure Linux</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ChronoZoom" title="ChronoZoom">ChronoZoom</a></li> <li><a href="/wiki/Extensible_Storage_Engine" title="Extensible Storage Engine">Extensible Storage Engine</a></li> <li><a href="/wiki/FlexWiki" class="mw-redirect" title="FlexWiki">FlexWiki</a></li> <li><a href="/wiki/FourQ" title="FourQ">FourQ</a></li> <li><a href="/wiki/Gollum_(software)" title="Gollum (software)">Gollum</a></li> <li><a href="/wiki/Project_Mu" class="mw-redirect" title="Project Mu">Project Mu</a></li> <li><a href="/wiki/ReactiveX" title="ReactiveX">ReactiveX</a></li> <li><a href="/wiki/SILK" title="SILK">SILK</a></li> <li><a href="/wiki/TLAPS" class="mw-redirect" title="TLAPS">TLAPS</a></li> <li><a href="/wiki/TPM_2.0_Reference_Implementation" class="mw-redirect" title="TPM 2.0 Reference Implementation">TPM 2.0 Reference Implementation</a></li> <li><a href="/wiki/WikiBhasha" title="WikiBhasha">WikiBhasha</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Open-source_license" title="Open-source license">Licenses</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Public_License" class="mw-redirect" title="Microsoft Public License">Microsoft Public License</a></li> <li><a href="/wiki/Microsoft_Reciprocal_License" class="mw-redirect" title="Microsoft Reciprocal License">Microsoft Reciprocal License</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Forge_(software)" title="Forge (software)">Forges</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/CodePlex" title="CodePlex">CodePlex</a></li> <li><a href="/wiki/GitHub" title="GitHub">GitHub</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/.NET_Foundation" title=".NET Foundation">.NET Foundation</a></li> <li><a href="/wiki/F_Sharp_Software_Foundation" title="F Sharp Software Foundation">F# Software Foundation</a></li> <li><a href="/wiki/Microsoft_Open_Specification_Promise" title="Microsoft Open Specification Promise">Microsoft Open Specification Promise</a></li> <li><a href="/wiki/Open_Letter_to_Hobbyists" class="mw-redirect" title="Open Letter to Hobbyists">Open Letter to Hobbyists</a></li> <li><a href="/wiki/Open_Source_Security_Foundation" title="Open Source Security Foundation">Open Source Security Foundation</a></li> <li><a href="/wiki/Outercurve_Foundation" title="Outercurve Foundation">Outercurve Foundation</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Microsoft_free_software" title="Category:Microsoft free software">Category</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Microsoft_Research_(MSR)" style="padding:3px"><table class="nowraplinks 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Microsoft_Research" title="Template:Microsoft Research"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Microsoft_Research" title="Template talk:Microsoft Research"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Microsoft_Research" title="Special:EditPage/Template:Microsoft Research"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Microsoft_Research_(MSR)" style="font-size:114%;margin:0 4em"><a href="/wiki/Microsoft_Research" title="Microsoft Research">Microsoft Research (MSR)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main<br />projects</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Languages, compilers</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bartok_(compiler)" title="Bartok (compiler)">Bartok</a></li> <li><a href="/wiki/Bosque_(programming_language)" title="Bosque (programming language)">Bosque</a></li> <li><a href="/wiki/C%CF%89" class="mw-redirect" title="Cω">Cω</a></li> <li><a href="/wiki/F*_(programming_language)" title="F* (programming language)">F*</a></li> <li><a href="/wiki/Lean_(proof_assistant)" title="Lean (proof assistant)">Lean</a></li> <li><a href="/wiki/P_(programming_language)" title="P (programming language)">P</a></li> <li><a href="/wiki/Project_Verona" title="Project Verona">Project Verona</a></li> <li><a href="/wiki/Microsoft_Phoenix" title="Microsoft Phoenix">Phoenix</a></li> <li><a href="/wiki/Polyphonic_C_Sharp" class="mw-redirect" title="Polyphonic C Sharp">Polyphonic C#</a></li> <li><a href="/wiki/SecPAL" title="SecPAL">SecPAL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Distributed_computing" title="Distributed computing">Distributed</a>–<a href="/wiki/Grid_computing" title="Grid computing">grid computing</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/BitVault" title="BitVault">BitVault</a></li> <li><a href="/wiki/Confidential_Consortium_Framework" title="Confidential Consortium Framework">Confidential Consortium Framework</a></li> <li><a href="/wiki/DeepSpeed" title="DeepSpeed">DeepSpeed</a></li> <li><a href="/wiki/Orleans_(software_framework)" title="Orleans (software framework)">Orleans</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Internet" title="Internet">Internet</a>, <a href="/wiki/Computer_network" title="Computer network">networking</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AjaxView" title="AjaxView">AjaxView</a></li> <li><a href="/wiki/Avalanche_(P2P)" title="Avalanche (P2P)">Avalanche</a></li> <li><a href="/wiki/Conference_XP" title="Conference XP">Conference XP</a></li> <li><a href="/wiki/Gazelle_(web_browser)" title="Gazelle (web browser)">Gazelle</a></li> <li><a href="/wiki/HoneyMonkey" title="HoneyMonkey">HoneyMonkey</a></li> <li><a href="/wiki/Penny_Black_(research_project)" title="Penny Black (research project)">Penny Black</a></li> <li><a href="/wiki/Wallop" title="Wallop">Wallop</a></li> <li><a href="/wiki/WikiBhasha" title="WikiBhasha">WikiBhasha</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other projects</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/Microsoft_Automatic_Graph_Layout" title="Microsoft Automatic Graph Layout">Automatic Graph Layout</a></li> <li><a href="/wiki/Microsoft_Cognitive_Toolkit" title="Microsoft Cognitive Toolkit">Cognitive Toolkit</a></li> <li><a href="/wiki/Project_Digits" title="Project Digits">Digits</a></li> <li><a href="/wiki/Microsoft_Holoportation" title="Microsoft Holoportation">Holoportation</a></li> <li><a href="/wiki/IllumiRoom" title="IllumiRoom">IllumiRoom</a></li> <li><a href="/wiki/Image_Composite_Editor" title="Image Composite Editor">Image Composite Editor</a></li> <li><a href="/wiki/Infer.NET" title="Infer.NET">Infer.NET</a></li> <li><a href="/wiki/LightGBM" title="LightGBM">LightGBM</a></li> <li><a href="/wiki/LiveStation" title="LiveStation">LiveStation</a></li> <li><a href="/wiki/MyLifeBits" title="MyLifeBits">MyLifeBits</a></li> <li><a href="/wiki/Neural_Network_Intelligence" title="Neural Network Intelligence">Neural Network Intelligence</a></li> <li><a href="/wiki/NodeXL" title="NodeXL">NodeXL</a></li> <li><a href="/wiki/OneFuzz" title="OneFuzz">OneFuzz</a></li> <li><a href="/wiki/PhotoDNA" title="PhotoDNA">PhotoDNA</a></li> <li><a href="/wiki/Microsoft_SEAL" title="Microsoft SEAL">SEAL</a></li> <li><a href="/wiki/SLAM_project" title="SLAM project">SLAM</a></li> <li><a href="/wiki/T2_Temporal_Prover" title="T2 Temporal Prover">T2 Temporal Prover</a></li> <li><a href="/wiki/WorldWide_Telescope" title="WorldWide Telescope">WorldWide Telescope</a></li> <li><a href="/wiki/Z3_Theorem_Prover" title="Z3 Theorem Prover">Z3 Theorem Prover</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Operating_system" title="Operating system">Operating systems</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Barrelfish_(operating_system)" title="Barrelfish (operating system)">Barrelfish</a></li> <li><a href="/wiki/HomeOS" title="HomeOS">HomeOS</a></li> <li><a href="/wiki/Midori_(operating_system)" title="Midori (operating system)">Midori</a></li> <li><a href="/wiki/Singularity_(operating_system)" title="Singularity (operating system)">Singularity</a></li> <li><a href="/wiki/Verve_(operating_system)" title="Verve (operating system)">Verve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/API" title="API">APIs</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/Accelerator_(library)" title="Accelerator (library)">Accelerator</a></li> <li><a href="/wiki/Dryad_(programming)" title="Dryad (programming)">Dryad</a></li> <li><a href="/wiki/Joins_(concurrency_library)" title="Joins (concurrency library)">Joins</a></li> <li><a href="/wiki/Mimalloc" title="Mimalloc">mimalloc</a></li> <li><a href="/wiki/SXM_(transactional_memory)" title="SXM (transactional memory)">SXM</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Launched as products</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a></li> <li><a href="/wiki/Microsoft_Comic_Chat" title="Microsoft Comic Chat">Comic Chat</a></li> <li><a href="/wiki/Microsoft_Detours" title="Microsoft Detours">Detours</a></li> <li><a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a></li> <li><a href="/wiki/Windows_Desktop_Gadgets" title="Windows Desktop Gadgets">Sideshow</a></li> <li><a href="/wiki/Microsoft_PixelSense" title="Microsoft PixelSense">PixelSense</a> (<a href="/wiki/TouchLight" title="TouchLight">TouchLight</a>)</li> <li><a href="/wiki/Microsoft_SenseCam" title="Microsoft SenseCam">SenseCam</a></li> <li><a href="/wiki/ClearType" title="ClearType">ClearType</a></li> <li><a href="/wiki/Group_Shot" title="Group Shot">Group Shot</a></li> <li><a href="/wiki/Allegiance_(video_game)" title="Allegiance (video game)">Allegiance</a></li> <li><a href="/wiki/TrueSkill" title="TrueSkill">TrueSkill</a></li> <li><a href="/wiki/Microsoft_Songsmith" class="mw-redirect" title="Microsoft Songsmith">Songsmith</a></li> <li><a href="/wiki/Xbox" title="Xbox">Xbox</a> <ul><li><a href="/wiki/Kinect" title="Kinect">Kinect</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">MSR Labs<br />applied<br />research</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microsoft_Live_Labs" title="Microsoft Live Labs">Live Labs</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Current</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/Microsoft_Live_Labs_Pivot" title="Microsoft Live Labs Pivot">Pivot</a></li> <li><a href="/wiki/Seadragon_Software" title="Seadragon Software">Seadragon</a> <ul><li><a href="/wiki/Deep_Zoom" title="Deep Zoom">Deep Zoom</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discontinued</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Live_Labs_Deepfish" title="Microsoft Live Labs Deepfish">Deepfish</a></li> <li><a href="/wiki/Microsoft_Live_Labs_Listas" title="Microsoft Live Labs Listas">Listas</a></li> <li><a href="/wiki/Live_Clipboard" title="Live Clipboard">Live Clipboard</a></li> <li><a href="/wiki/Photosynth" title="Photosynth">Photosynth</a></li> <li><a href="/wiki/Microsoft_Live_Labs_Volta" title="Microsoft Live Labs Volta">Volta</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Microsoft_FUSE_Labs" title="Microsoft FUSE Labs">FUSE Labs</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/Docs.com" title="Docs.com">Docs.com</a></li> <li><a href="/wiki/Kodu_Game_Lab" title="Kodu Game Lab">Kodu</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other labs</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Microsoft_Academic_Search" title="Microsoft Academic Search">Academic Search</a></li> <li><a href="/wiki/Microsoft_adCenter_Labs" title="Microsoft adCenter Labs">adCenter Labs</a></li> <li><a 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