A Formulation of Composition for Cellular Automata on Groups
We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and...
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| Veröffentlicht in: | IEICE Transactions on Information and Systems 2014/03/01, Vol.E97.D(3), pp.448-454 |
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| container_title | IEICE Transactions on Information and Systems |
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| creator | INOKUCHI, Shuichi ITO, Takahiro FUJIO, Mitsuhiko MIZOGUCHI, Yoshihiro |
| description | We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. We also show our formulation contains the representation using formal power series for linear cellular automata in Manzini [6]. |
| doi_str_mv | 10.1587/transinf.E97.D.448 |
| format | Article |
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A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. 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We also show our formulation contains the representation using formal power series for linear cellular automata in Manzini [6].</description><subject>automata</subject><subject>Cellular automata</subject><subject>Division</subject><subject>Formulations</subject><subject>groups</subject><subject>models of computation</subject><subject>Nonlinearity</subject><subject>Power series</subject><subject>Representations</subject><subject>Unions</subject><issn>0916-8532</issn><issn>1745-1361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpdkE1LxDAQhoMouK7-AU89emnNNEmbgJel-yUseNFziGmiXdqmJunBf2_d1RU8DcP7PsPwIHQLOAPGy_voVR-a3mYrUWbLjFJ-hmZQUpYCKeAczbCAIuWM5JfoKoQ9xsBzYDP0sEjWzndjq2Lj-sTZpHLd4EJzWK3zSWXadop9shij61RUyRRsvBuHcI0urGqDufmZc_SyXj1X23T3tHmsFrtUM1bE1Oa11bkpKbaclAU3pqasNAQXNTdKUUF1gXPDiX4FzoAKrGqlqSCABbGiJHN0d7w7ePcxmhBl1wQ9_aV648YggVGggEkhpmp-rGrvQvDGysE3nfKfErD8ViV_VclJlVzKSdUEbY_QPkT1Zk6I8rHRrfmPkD_0VNHvykvTky-rPHk5</recordid><startdate>2014</startdate><enddate>2014</enddate><creator>INOKUCHI, Shuichi</creator><creator>ITO, Takahiro</creator><creator>FUJIO, Mitsuhiko</creator><creator>MIZOGUCHI, Yoshihiro</creator><general>The Institute of Electronics, Information and Communication Engineers</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2014</creationdate><title>A Formulation of Composition for Cellular Automata on Groups</title><author>INOKUCHI, Shuichi ; ITO, Takahiro ; FUJIO, Mitsuhiko ; MIZOGUCHI, Yoshihiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c556t-f2dfc2e740f83768eed457e306d8eaa494c602e83cb1851490adac4931093f973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>automata</topic><topic>Cellular automata</topic><topic>Division</topic><topic>Formulations</topic><topic>groups</topic><topic>models of computation</topic><topic>Nonlinearity</topic><topic>Power series</topic><topic>Representations</topic><topic>Unions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>INOKUCHI, Shuichi</creatorcontrib><creatorcontrib>ITO, Takahiro</creatorcontrib><creatorcontrib>FUJIO, Mitsuhiko</creatorcontrib><creatorcontrib>MIZOGUCHI, Yoshihiro</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEICE Transactions on Information and Systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>INOKUCHI, Shuichi</au><au>ITO, Takahiro</au><au>FUJIO, Mitsuhiko</au><au>MIZOGUCHI, Yoshihiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Formulation of Composition for Cellular Automata on Groups</atitle><jtitle>IEICE Transactions on Information and Systems</jtitle><addtitle>IEICE Trans. Inf. & Syst.</addtitle><date>2014</date><risdate>2014</risdate><volume>E97.D</volume><issue>3</issue><spage>448</spage><epage>454</epage><pages>448-454</pages><issn>0916-8532</issn><eissn>1745-1361</eissn><abstract>We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. 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| source | J-STAGE (Japan Science & Technology Information Aggregator, Electronic) Freely Available Titles - Japanese; EZB-FREE-00999 freely available EZB journals |
| subjects | automata Cellular automata Division Formulations groups models of computation Nonlinearity Power series Representations Unions |
| title | A Formulation of Composition for Cellular Automata on Groups |
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