{"id":6347,"date":"2018-05-30T13:38:37","date_gmt":"2018-05-30T12:38:37","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6347"},"modified":"2022-12-03T23:00:29","modified_gmt":"2022-12-03T22:00:29","slug":"langages-reguliers-et-expressions-regulieres","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/lenguajes-regulares-y-expresiones-regulares\/","title":{"rendered":"Lenguajes regulares y expresiones regulares"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6347\" class=\"elementor elementor-6347\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4246d1c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4246d1c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6c90b6f\" data-id=\"6c90b6f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2a08eaf elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a08eaf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Teor\u00eda del lenguaje<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9ee40a5\" data-id=\"9ee40a5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-546da1c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"546da1c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8c2eb5d\" data-id=\"8c2eb5d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b61443a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b61443a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Grammaire_r%C3%A9guli%C3%A8re\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-38b7465 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"38b7465\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9e9f54b\" data-id=\"9e9f54b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cb074cd elementor-widget elementor-widget-progress\" data-id=\"cb074cd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"progress.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<span class=\"elementor-title\" id=\"elementor-progress-bar-cb074cd\">\n\t\t\t\tDificultad\t\t\t<\/span>\n\t\t\n\t\t<div aria-labelledby=\"elementor-progress-bar-cb074cd\" class=\"elementor-progress-wrapper\" role=\"progressbar\" aria-valuemin=\"0\" aria-valuemax=\"100\" aria-valuenow=\"25\" aria-valuetext=\"25% (Facile)\">\n\t\t\t<div class=\"elementor-progress-bar\" data-max=\"25\">\n\t\t\t\t<span class=\"elementor-progress-text\">F\u00e1cil<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-progress-percentage\">25%<\/span>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-34a56aa3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"34a56aa3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-244fb042\" data-id=\"244fb042\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-100384e8 elementor-widget elementor-widget-text-editor\" data-id=\"100384e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/lenguajes-regulares-y-expresiones-regulares\/#Langages-reguliers-et-expressions-regulieres\" >Lenguajes regulares y expresiones regulares<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/lenguajes-regulares-y-expresiones-regulares\/#Langage-et-expression\" >Lenguaje y expresion<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/lenguajes-regulares-y-expresiones-regulares\/#Processus-de-creation-dautomate-a-partir-dune-expression-reguliere\" >Proceso de creaci\u00f3n de un aut\u00f3mata a partir de una expresi\u00f3n regular.<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Langages-reguliers-et-expressions-regulieres\"><\/span>Lenguajes regulares y expresiones regulares<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Hay dos tipos de expresiones regulares.<\/p>\n\n<p class=\"wp-block-paragraph\">Recordamos que un <a href=\"https:\/\/complex-systems-ai.com\/es\/teoria-del-lenguaje\/tipos-de-gramaticas\/\">gram\u00e1tica<\/a> G1 = (T, N, S, R) es una expresi\u00f3n regular por la derecha si las reglas de R son de la forma: A \u2192 aB o A \u2192 a con A, B \u2208 N y a \u2208 T.<\/p>\n\n<p class=\"wp-block-paragraph\">Recuerde que una gram\u00e1tica G2 = (T, N, S, R) es una expresi\u00f3n regular de la izquierda si las reglas de R son de la forma: A \u2192 Ba o A \u2192 a con A, B \u2208 N y a \u2208 T.<\/p>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">Un idioma es regular o racional si y solo si existe una gram\u00e1tica regular que genera este idioma.<\/div>\n\n<p class=\"wp-block-paragraph\">La ventaja de distinguir gram\u00e1ticas regulares a la derecha o a la izquierda aparece durante el an\u00e1lisis: si leemos los s\u00edmbolos de la palabra a analizar de izquierda a derecha, entonces<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Se utilizar\u00e1 una gram\u00e1tica normal de la mano derecha para un an\u00e1lisis de arriba hacia abajo, desde el axioma hasta la palabra.<\/li>\n<li>Se utilizar\u00e1 una gram\u00e1tica normal de la mano izquierda para un an\u00e1lisis de abajo hacia arriba, desde la palabra hasta el axioma.<\/li>\n<\/ul>\n\n<p class=\"wp-block-paragraph\">Por ejemplo, para analizar la palabra aaabb con la gram\u00e1tica G1, construiremos la derivaci\u00f3n S1 \u21d2 aS1 \u21d2 aaS1 \u21d2 aaaU1 \u21d2 aaabU1 \u21d2 aaabb; mientras que para analizar esta palabra con la gram\u00e1tica G2, construiremos la derivaci\u00f3n aaabb \u21d0 U2aabb \u21d0 U2abb \u21d0 U2bb \u21d0 S2b \u21d0 S2.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Langage-et-expression\"><\/span>Lenguaje y expresion<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">\n<p>Una expresi\u00f3n E es una expresi\u00f3n regular en un alfabeto A si y solo si:<\/p>\n<ul>\n<li>E = \u2205 o<\/li>\n<li>E = \u03b5 o<\/li>\n<li>E = a con a \u2208 A o<\/li>\n<li>E = E1 | E2 y E1 y E2 son dos expresiones regulares en A o<\/li>\n<li>E = E1.E2 y E1 y E2 son dos expresiones regulares en A o<\/li>\n<li>E = E<sup>\u2217<\/sup><sub>1<\/sub> Verano<sub>1<\/sub> es una expresi\u00f3n regular en A<\/li>\n<\/ul>\n<\/div>\n\n<p class=\"wp-block-paragraph\">Los operadores \u2217 ,. y | tienen prioridad decreciente. Si es necesario, se pueden agregar par\u00e9ntesis.<\/p>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">\n<p>El lenguaje L (E) descrito por una expresi\u00f3n regular E definida en un alfabeto A est\u00e1 definido por<\/p>\n<ul>\n<li>L (E) = \u2205 si E = \u2205,<\/li>\n<li>L (E) = {\u03b5} si E = \u03b5,<\/li>\n<li>L (E) = {a} si E = a,<\/li>\n<li>L (E) = L (E1) \u222a L (E2) si E = E1 | E2,<\/li>\n<li>L (E) = L (E1) .L (E2) si E = E1.E2,<\/li>\n<li>L (E) = L (E1)<sup>\u2217<\/sup>\u00a0si E = E<sup>\u2217<\/sup><sub>1<\/sub> Verano<sub>1<\/sub> es una expresi\u00f3n regular en A.<\/li>\n<\/ul>\n<\/div>\n\n<p class=\"wp-block-paragraph\">La equivalencia entre expresiones regulares y lenguajes regulares se establece por las siguientes dos implicaciones:<\/p>\n\n<ul class=\"wp-block-list\">\n<li>Cualquier expresi\u00f3n regular describe un idioma regular.<\/li>\n<li>Cualquier idioma regular puede describirse mediante una expresi\u00f3n regular.<\/li>\n<\/ul>\n\n<p class=\"wp-block-paragraph\">Lista de equivalencias trivial:<\/p>\n\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6501\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/07\/langage25.png\" alt=\"expresiones regulares\" width=\"823\" height=\"198\" title=\"\"><\/figure>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Processus-de-creation-dautomate-a-partir-dune-expression-reguliere\"><\/span>Proceso de creaci\u00f3n de un aut\u00f3mata a partir de una expresi\u00f3n regular.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/10\/langen2.png\" alt=\"expresi\u00f3n regular\" width=\"336\" height=\"362\" title=\"\"><\/figure>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Language Theory Wiki Inicio Dificultad F\u00e1cil 25% Lenguajes Regulares y Expresiones Regulares Hay dos tipos de expresiones regulares. Recordemos que una gram\u00e1tica G1... <\/p>","protected":false},"author":1,"featured_media":0,"parent":5028,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6347","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=6347"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6347\/revisions"}],"predecessor-version":[{"id":18583,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6347\/revisions\/18583"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/5028"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=6347"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}