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mw-first-heading"><span class="mw-page-title-main">Terminal and nonterminal symbols</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 13 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-13" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">13 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%B1%D9%85%D9%88%D8%B2_%D8%A7%D9%84%D8%B7%D8%B1%D9%81%D9%8A%D8%A9_%D9%88%D8%BA%D9%8A%D8%B1_%D8%A7%D9%84%D8%B7%D8%B1%D9%81%D9%8A%D8%A9" title="الرموز الطرفية وغير الطرفية – Arabic" lang="ar" hreflang="ar" data-title="الرموز الطرفية وغير الطرفية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Zavr%C5%A1ni_i_nezavr%C5%A1ni_znakovi" title="Završni i nezavršni znakovi – Bosnian" lang="bs" hreflang="bs" data-title="Završni i nezavršni znakovi" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Termin%C3%A1ln%C3%AD_a_netermin%C3%A1ln%C3%AD_symbol" title="Terminální a neterminální symbol – Czech" lang="cs" hreflang="cs" data-title="Terminální a neterminální symbol" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%85%D8%A7%D8%AF%D9%87%D8%A7%DB%8C_%D9%BE%D8%A7%DB%8C%D8%A7%D9%86%DB%8C_%D9%88_%D8%BA%DB%8C%D8%B1%D9%BE%D8%A7%DB%8C%D8%A7%D9%86%DB%8C" title="نمادهای پایانی و غیرپایانی – Persian" lang="fa" hreflang="fa" data-title="نمادهای پایانی و غیرپایانی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Symboles_terminaux_et_non_terminaux" title="Symboles terminaux et non terminaux – French" lang="fr" hreflang="fr" data-title="Symboles terminaux et non terminaux" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Zavr%C5%A1ni_i_nezavr%C5%A1ni_znakovi" title="Završni i nezavršni znakovi – Croatian" lang="hr" hreflang="hr" data-title="Završni i nezavršni znakovi" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Terminale_en_niet-terminale_symbolen" title="Terminale en niet-terminale symbolen – Dutch" lang="nl" hreflang="nl" data-title="Terminale en niet-terminale symbolen" 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/%E7%B5%82%E7%AB%AF%E8%A8%98%E5%8F%B7%E3%81%A8%E9%9D%9E%E7%B5%82%E7%AB%AF%E8%A8%98%E5%8F%B7" title="終端記号と非終端記号 – Japanese" lang="ja" hreflang="ja" data-title="終端記号と非終端記号" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/S%C3%ADmbolos_terminais_e_n%C3%A3o_terminais" title="Símbolos terminais e não terminais – Portuguese" lang="pt" hreflang="pt" data-title="Símbolos terminais e não terminais" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%97%D0%B0%D0%B2%D1%80%D1%88%D0%BD%D0%B8_%D0%B8_%D0%BD%D0%B5%D0%B7%D0%B0%D0%B2%D1%80%D1%88%D0%BD%D0%B8_%D1%81%D0%B8%D0%BC%D0%B1%D0%BE%D0%BB%D0%B8" title="Завршни и незавршни симболи – Serbian" lang="sr" hreflang="sr" data-title="Завршни и незавршни симболи" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Zavr%C5%A1ni_i_nezavr%C5%A1ni_znakovi" title="Završni i nezavršni znakovi – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Završni i nezavršni znakovi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-uk badge-Q70893996 mw-list-item" title=""><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%80%D0%BC%D1%96%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%96_%D1%82%D0%B0_%D0%BD%D0%B5%D1%82%D0%B5%D1%80%D0%BC%D1%96%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%96_%D1%81%D0%B8%D0%BC%D0%B2%D0%BE%D0%BB%D0%B8" title="Термінальні та нетермінальні символи – Ukrainian" lang="uk" hreflang="uk" data-title="Термінальні та нетермінальні символи" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link 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</div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to 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src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Terminal_and_non-terminal_symbols_example.png/450px-Terminal_and_non-terminal_symbols_example.png" decoding="async" width="450" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Terminal_and_non-terminal_symbols_example.png/675px-Terminal_and_non-terminal_symbols_example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Terminal_and_non-terminal_symbols_example.png/900px-Terminal_and_non-terminal_symbols_example.png 2x" data-file-width="1651" data-file-height="874" /></a><figcaption>The string "the dog ate the bone" was created using production rules that replaced non-terminal with terminal symbols.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>In <a href="/wiki/Formal_languages" class="mw-redirect" title="Formal languages">formal languages</a>, <b>terminal and nonterminal symbols</b> are the <a href="/wiki/Lexical_item" title="Lexical item">lexical elements</a> used in specifying the <a href="/wiki/Production_(computer_science)" title="Production (computer science)">production rules</a> constituting a <a href="/wiki/Formal_grammar" title="Formal grammar">formal grammar</a>. <i>Terminal symbols</i> are the elementary symbols of the <a href="/wiki/Formal_language" title="Formal language"> language</a> defined as part of a formal grammar. <i>Nonterminal symbols</i> (or <i>syntactic variables</i>) are replaced by groups of terminal symbols according to the production rules. </p><p>The terminals and nonterminals of a particular grammar are in two <a href="/wiki/Disjoint_sets" title="Disjoint sets"> completely separate sets</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Terminal_symbols">Terminal symbols</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Terminal_and_nonterminal_symbols&action=edit&section=1" title="Edit section: Terminal symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Terminal symbols are symbols that may appear in the outputs of the production rules of a formal grammar and which cannot be changed using the rules of the grammar. Applying the rules recursively to a source string of symbols will usually terminate in a final output string consisting only of terminal symbols. </p><p>Consider a grammar defined by two rules. In this grammar, the symbol <code>Б</code> is a terminal symbol and <code>Ψ</code> is both a non-terminal symbol and the start symbol. The production rules for creating strings are as follows: </p> <ol><li>The symbol <code>Ψ</code> can become <code>Б</code><code>Ψ</code></li> <li>The symbol <code>Ψ</code> can become <code>Б</code></li></ol> <p>Here <code>Б</code> is a terminal symbol because no rule exists which would change it into something else. On the other hand, <code>Ψ</code> has two rules that can change it, thus it is nonterminal. A <a href="/wiki/Formal_language" title="Formal language">formal language</a> defined or <i>generated</i> by a particular grammar is the set of strings that can be produced by the grammar <i>and that consist only of terminal symbols</i>. Diagram 1 illustrates a string that can be produced with this grammar. </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Terminal_and_non-terminal_symbols_example_number_two.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Terminal_and_non-terminal_symbols_example_number_two.png/350px-Terminal_and_non-terminal_symbols_example_number_two.png" decoding="async" width="350" height="192" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Terminal_and_non-terminal_symbols_example_number_two.png/525px-Terminal_and_non-terminal_symbols_example_number_two.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/Terminal_and_non-terminal_symbols_example_number_two.png/700px-Terminal_and_non-terminal_symbols_example_number_two.png 2x" data-file-width="1522" data-file-height="834" /></a><figcaption>Diagram 1. The string <code>Б Б Б Б</code> was formed by the grammar defined by the given production rules. This grammar can create strings with any number of the symbol Б</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Nonterminal_symbols">Nonterminal symbols</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Terminal_and_nonterminal_symbols&action=edit&section=2" title="Edit section: Nonterminal symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nonterminal symbols are those symbols that can be replaced. They may also be called simply <i>syntactic variables</i>. A formal grammar includes a <i>start symbol</i>, a designated member of the set of nonterminals from which all the strings in the language may be derived by successive applications of the production rules. In fact, the language defined by a grammar is precisely the set of <i>terminal</i> strings that can be so derived. </p><p><a href="/wiki/Context-free_grammar" title="Context-free grammar">Context-free grammars</a> are those grammars in which the left-hand side of each production rule consists of only a single nonterminal symbol. This restriction is non-trivial; not all languages can be generated by context-free grammars. Those that can are called context-free languages. These are exactly the languages that can be recognized by a non-deterministic <a href="/wiki/Push_down_automaton" class="mw-redirect" title="Push down automaton">push down automaton</a>. Context-free languages are the theoretical basis for the syntax of most <a href="/wiki/Programming_languages" class="mw-redirect" title="Programming languages">programming languages</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Production_rules">Production rules</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Terminal_and_nonterminal_symbols&action=edit&section=3" title="Edit section: Production rules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A grammar is defined by <a href="/wiki/Production_(computer_science)" title="Production (computer science)">production rules</a> (or just 'productions') that specify which symbols may replace which other symbols; these rules may be used to generate strings, or to parse them. Each such rule has a <i>head</i>, or left-hand side, which consists of the string that may be replaced, and a <i>body</i>, or right-hand side, which consists of a string that may replace it. Rules are often written in the form <i>head</i> → <i>body</i>; e.g., the rule <i>a</i> → <i>b</i> specifies that <i>a</i> can be replaced by <i>b</i>. </p><p>In the classic formalization of generative grammars first proposed by <a href="/wiki/Noam_Chomsky" title="Noam Chomsky">Noam Chomsky</a> in the 1950s,<sup id="cite_ref-Chomsky1956_2-0" class="reference"><a href="#cite_note-Chomsky1956-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Chomsky1957_3-0" class="reference"><a href="#cite_note-Chomsky1957-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> a grammar <i>G</i> consists of the following components: </p> <ul><li>A finite set <span class="texhtml mvar" style="font-style:italic;">N</span> of <i>nonterminal symbols</i>.</li> <li>A finite set <span class="texhtml">Σ</span> of <i>terminal symbols</i> that is <a href="/wiki/Disjoint_sets" title="Disjoint sets">disjoint</a> from <span class="texhtml mvar" style="font-style:italic;">N</span>.</li> <li>A finite set <span class="texhtml mvar" style="font-style:italic;">P</span> of <i>production rules</i>, each rule of the form</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\Sigma \cup N)^{*}N(\Sigma \cup N)^{*}\rightarrow (\Sigma \cup N)^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo>∪</mo> <mi>N</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mi>N</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo>∪</mo> <mi>N</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo>∪</mo> <mi>N</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\Sigma \cup N)^{*}N(\Sigma \cup N)^{*}\rightarrow (\Sigma \cup N)^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c629b18435275083d7d4893045ac96eb9e21a868" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.241ex; height:2.843ex;" alt="{\displaystyle (\Sigma \cup N)^{*}N(\Sigma \cup N)^{*}\rightarrow (\Sigma \cup N)^{*}}"></span></dd></dl></dd> <dd>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/002b545cd6a6f230c91717f3321b3288a405f6a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.054ex; height:2.176ex;" alt="{\displaystyle {}^{*}}"></span> is the <a href="/wiki/Kleene_star" title="Kleene star">Kleene star</a> operator and <span class="texhtml">∪</span> denotes <a href="/wiki/Union_(set_theory)" title="Union (set theory)">set union</a>, so <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\Sigma \cup N)^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">Σ</mi> <mo>∪</mo> <mi>N</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\Sigma \cup N)^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/428bb4332445f3207ebd42f751f0368473db1ded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.188ex; height:2.843ex;" alt="{\displaystyle (\Sigma \cup N)^{*}}"></span> represents zero or more symbols, and <span class="texhtml mvar" style="font-style:italic;">N</span> means one <i>nonterminal</i> symbol. That is, each production rule maps from one string of symbols to another, where the first string contains at least one nonterminal symbol. In the case that the body consists solely of the <a href="/wiki/Empty_string" title="Empty string">empty string</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup>, it may be denoted with a special notation (often <span class="texhtml">Λ</span>, <span class="texhtml mvar" style="font-style:italic;">e</span> or <span class="texhtml mvar" style="font-style:italic;">ε</span>) in order to avoid confusion.</dd></dl> <ul><li>A distinguished symbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\in N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>∈</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\in N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2825a0c08fd40c09a8c56df85454e574e1d4453f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.404ex; height:2.176ex;" alt="{\displaystyle S\in N}"></span> that is the <i>start symbol</i>.</li></ul> <p>A grammar is formally defined as the ordered quadruple <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle N,\Sigma ,P,S\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>N</mi> <mo>,</mo> <mi mathvariant="normal">Σ</mi> <mo>,</mo> <mi>P</mi> <mo>,</mo> <mi>S</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle N,\Sigma ,P,S\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28dd6e763572497c161b87549baae30b0c6c2556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.897ex; height:2.843ex;" alt="{\displaystyle \langle N,\Sigma ,P,S\rangle }"></span>. Such a formal grammar is often called a <a href="/wiki/Rewriting_system" class="mw-redirect" title="Rewriting system">rewriting system</a> or a <a href="/wiki/Phrase_structure_grammar" title="Phrase structure grammar">phrase structure grammar</a> in the literature.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Terminal_and_nonterminal_symbols&action=edit&section=4" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Backus%E2%80%93Naur_form" title="Backus–Naur form">Backus–Naur form</a> is a notation for expressing certain grammars. For instance, the following production rules in Backus-Naur form are used to represent an integer (which may be signed): </p> <div class="mw-highlight mw-highlight-lang-bnf mw-content-ltr" dir="ltr"><pre><span></span><span class="p"><</span><span class="nc">digit</span><span class="p">></span> <span class="o">::=</span> '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' <span class="p"><</span><span class="nc">integer</span><span class="p">></span> <span class="o">::=</span> ['-'] <span class="p"><</span><span class="nc">digit</span><span class="p">></span> {<span class="p"><</span><span class="nc">digit</span><span class="p">></span>} </pre></div> <p>In this example, the symbols (<style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">-,0,1,2,3,4,5,6,7,8,9</span>) are terminal symbols and <code class="nowrap" style=""><digit></code> and <code class="nowrap" style=""><integer></code> are nonterminal symbols. <sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup> </p><p>Another example is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {S -> cAd}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> <mo stretchy="false">⟶</mo> <mtext>cAd</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {S -> cAd}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81b0bbc06c5c55443fe618830452fe1fec452a30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.456ex; height:2.176ex;" alt="{\displaystyle {\ce {S -> cAd}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A -> a | ab}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mo stretchy="false">⟶</mo> <mtext>a</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mtext>ab</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A -> a | ab}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bc35575599cff25cec14db45cd81bf1f8a84197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.103ex; height:2.843ex;" alt="{\displaystyle {\ce {A -> a | ab}}}"></span></dd></dl> <p>In this example, the symbols <span class="texhtml">a,b,c,d</span> are terminal symbols and <span class="texhtml">S,A</span> are nonterminal symbols. </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=Terminal_and_nonterminal_symbols&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Alphabet_(formal_languages)" title="Alphabet (formal languages)">Alphabet (formal languages)</a></li> <li><a href="/wiki/Chomsky_Hierarchy" class="mw-redirect" title="Chomsky Hierarchy">Chomsky Hierarchy</a></li> <li><a href="/wiki/Recursive_grammar" title="Recursive grammar">Recursive grammar</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Terminal_and_nonterminal_symbols&action=edit&section=6" title="Edit section: Notes"><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-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">It contains no symbols at all.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">This example supports strings with leading zeroes like "0056" or "0000", as well as negative zero strings like "-0" and "-00000".</span> </li> </ol></div></div> <p><br /> </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=Terminal_and_nonterminal_symbols&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Rosen, K. H. (2012). Discrete mathematics and its applications. McGraw-Hill. pages 847-851</span> </li> <li id="cite_note-Chomsky1956-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chomsky1956_2-0">^</a></b></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 id="CITEREFChomsky,_Noam1956" class="citation journal cs1">Chomsky, Noam (1956). "Three Models for the Description of Language". <i><a href="/wiki/IRE_Transactions_on_Information_Theory" class="mw-redirect" title="IRE Transactions on Information Theory">IRE Transactions on Information Theory</a></i>. <b>2</b> (3): 113–123. <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%2FTIT.1956.1056813">10.1109/TIT.1956.1056813</a>. <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:19519474">19519474</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IRE+Transactions+on+Information+Theory&rft.atitle=Three+Models+for+the+Description+of+Language&rft.volume=2&rft.issue=3&rft.pages=113-123&rft.date=1956&rft_id=info%3Adoi%2F10.1109%2FTIT.1956.1056813&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A19519474%23id-name%3DS2CID&rft.au=Chomsky%2C+Noam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerminal+and+nonterminal+symbols" class="Z3988"></span></span> </li> <li id="cite_note-Chomsky1957-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chomsky1957_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChomsky,_Noam1957" class="citation book cs1">Chomsky, Noam (1957). <i><a href="/wiki/Syntactic_Structures" title="Syntactic Structures">Syntactic Structures</a></i>. The Hague: <a href="/wiki/Mouton_de_Gruyter" class="mw-redirect" title="Mouton de Gruyter">Mouton</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Syntactic+Structures&rft.place=The+Hague&rft.pub=Mouton&rft.date=1957&rft.au=Chomsky%2C+Noam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerminal+and+nonterminal+symbols" 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 id="CITEREFGinsburg1975" class="citation book cs1"><a href="/wiki/Seymour_Ginsburg" title="Seymour Ginsburg">Ginsburg, Seymour</a> (1975). <i>Algebraic and automata theoretic properties of formal languages</i>. North-Holland. pp. 8–9. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7204-2506-9" title="Special:BookSources/0-7204-2506-9"><bdi>0-7204-2506-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebraic+and+automata+theoretic+properties+of+formal+languages&rft.pages=8-9&rft.pub=North-Holland&rft.date=1975&rft.isbn=0-7204-2506-9&rft.aulast=Ginsburg&rft.aufirst=Seymour&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerminal+and+nonterminal+symbols" 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 id="CITEREFHarrison1978" class="citation book cs1"><a href="/wiki/Michael_A._Harrison" title="Michael A. Harrison">Harrison, Michael A.</a> (1978). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontofo00harr_425"><i>Introduction to Formal Language Theory</i></a></span>. Reading, Mass.: Addison-Wesley Publishing Company. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontofo00harr_425/page/n14">13</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-02955-3" title="Special:BookSources/0-201-02955-3"><bdi>0-201-02955-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Formal+Language+Theory&rft.place=Reading%2C+Mass.&rft.pages=13&rft.pub=Addison-Wesley+Publishing+Company&rft.date=1978&rft.isbn=0-201-02955-3&rft.aulast=Harrison&rft.aufirst=Michael+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontofo00harr_425&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerminal+and+nonterminal+symbols" class="Z3988"></span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Terminal_and_nonterminal_symbols&oldid=1235090050">https://en.wikipedia.org/w/index.php?title=Terminal_and_nonterminal_symbols&oldid=1235090050</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Formal_languages" title="Category:Formal languages">Formal languages</a></li><li><a href="/wiki/Category:Pattern_matching" title="Category:Pattern matching">Pattern matching</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 17 July 2024, at 16:43<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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