{"id":14653,"date":"2022-05-20T19:55:11","date_gmt":"2022-05-20T23:55:11","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14653"},"modified":"2026-06-09T14:37:15","modified_gmt":"2026-06-09T18:37:15","slug":"tr-26-on-the-essential-equivalence-of-two-families-of-learning-automata","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1983\/tr-26-on-the-essential-equivalence-of-two-families-of-learning-automata\/","title":{"rendered":"TR-26: On the Essential Equivalence of Two Families of Learning Automata"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-26: On the Essential Equivalence of Two Families of Learning Automata\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1983\/\">Technical Report<\/a>\u00a0<strong>TR-26<\/strong><br>May 1983<\/p>\n\n\n\n<h2 id=\"on-the-essential-equivalence-of-two-families-of-learning-automata\" class=\"wp-block-heading\">On the Essential Equivalence of Two Families of Learning Automata<\/h2>\n\n\n\n<p>M.A.L. Thathachar &amp; B.J. Oommen<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>Fixed Structure Stochastic Automata (FSSA) have been used to learn the best of a finite set of actions by interacting with a random environment. Two families of such automata are the Tsetlin Automata and the Krylov Automata. In this paper, it is shown that a Krylov Automaton which possesses a certain number of states and which interacts with an environment E1 is equivalent to a Tsetlin Automation possessing the same number of states but which interacts with an environment E2. The relationship between the environments has also been derived. A tremendous gain in computation can thus be obtained in the study of the Krylov Automaton (which is essentially stochastic) by studying the corresponding deterministic Tsetlin automaton in the modified environment.&nbsp; Apart from being of computational significance, this demonstrates a new way of studying certain families of Fixed Structure Stochastic Automata (FSSA) using deterministic automata thus simplifying both the analysis and the computation.<\/p>\n\n\n\n<h3 id=\"download\" class=\"wp-block-heading\">Download<\/h3>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-26.pdf\">TR-26.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report\u00a0TR-26May 1983 On the Essential Equivalence of Two Families of Learning Automata M.A.L. Thathachar &amp; B.J. Oommen Abstract Fixed Structure Stochastic Automata (FSSA) have been used to learn the best of a finite set of actions by interacting with a random environment. Two families of such automata are the Tsetlin Automata and the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11785,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[88],"class_list":["post-14653","page","type-page","status-publish","hentry","cu_page_type-technical-report"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14653","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14653"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14653\/revisions"}],"predecessor-version":[{"id":24567,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14653\/revisions\/24567"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11785"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14653"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}