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A characterization of automata and a direct product decomposition

Yoshifumi Masunaga, Shoichi Noguchi, Juro Oizumi
<span title="">1976</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
by semigroups with left identity, monoids, commutative semigroups with identity, right groups, right zero semigroups, groups, and Abelian groups, respectively.  ...  The classes of automata characterized by certain semigroups are investigated: It is shown that the classes of cyclic quasi-state-independent automata, cyclic quasi-stateindependent automata of monoid type  ...  groups, right zero semigroups, groups, and Abelian groups, respectively.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(76)80052-9">doi:10.1016/s0022-0000(76)80052-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kfnkuca7o5fn3asadftju2m7bq">fatcat:kfnkuca7o5fn3asadftju2m7bq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003024012/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/c2b/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAyMjAwMDA3NjgwMDUyOQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/25/c2255d9adbfa697275772b87604bd7970e6848c0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(76)80052-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Polynomial-time algorithms for testing strong isomorphism and computing the automorphism group of R-strongly connected automata

Shuhua Zhang
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The class of R-strongly connected automata includes strongly connected, permutation, group type, state-independent and right simple type automata.  ...  All rights reserved  ...  A =(S, C, M) is called a right simple (right group, group) type automaton if Z(A) is a right simple semigroup (right group, group).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(92)90268-k">doi:10.1016/0304-3975(92)90268-k</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hwlo5g455ram3g26pu7caaihsa">fatcat:hwlo5g455ram3g26pu7caaihsa</a> </span>
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The amalgamation of automata

Toshimasa Watanabe, Shoichi Noguchi
<span title="">1977</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
We demonstrate in this paper a direct product decomposability of automata, and discuss the hierarchy of automata which is characterized by the characteristic semigroups.  ...  By introducing the concept of the amalgamation of automata, we discuss their structure and classification in terms of characteristic semigroups, when the input is a free semigroup generated by a set of  ...  is properly included by that of right group type automata.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(77)80024-x">doi:10.1016/s0022-0000(77)80024-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hhtnwww2tfc25lamx2nguluhuy">fatcat:hhtnwww2tfc25lamx2nguluhuy</a> </span>
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Page 6560 of Mathematical Reviews Vol. , Issue 87k [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Toshimasa Watanabe (Hiroshima) 87k:68109 Katsura, Masashi (J-KSU) 87k:68111 A note on regularity of group-matrix type automata. Papers on automata and languages, VII, 49-66, DM, 85-1, Karl Marz Univ.  ...  A group-matrix type automaton A of order n on G, also called simply an (n,G)-automaton (for a positive integer n and a finite group G), is said to be regular if A is strongly connected and its automorphism  ... 
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Page 4578 of Mathematical Reviews Vol. , Issue 98G [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We exhibit a formal correspondence between the two evaluation modes on trees (ascending and descending) and the two on words (right- to-left and left-to-right).  ...  ) Automorphism groups of context-free graphs.  ... 
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<a target="_blank" rel="noopener" href="https://archive.org/details/sim_mathematical-reviews_1998-07_98g/page/4578" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_mathematical-reviews_1998-07_98g/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Page 7774 of Mathematical Reviews Vol. , Issue 96m [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
These automata are called right group-type au- tomata. We prove that an A-finite automaton is state-independent if and only if it is right group-type.  ...  to A is a right zero decomposition of pairwise isomorphic group-type quasi- automata.  ... 
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Page 384 of Mathematical Reviews Vol. 25, Issue 2 [page]

<span title="">1963</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Section 4 explores further the relationship between automata and semi-groups (for example, what type of homomorphisms of the latter are induced by homo- morphisms of the former).  ...  Section 1 is concerned with homomorphisms, iso- morphisms, and equivalences of automata. The focus is upon two types of automata, Mealy machines and Moore machines.  ... 
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2D-Cellular Automata: Evolution and Boundary Defects

<span title="2017-07-05">2017</span> <i title="International Journal of Science and Research"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/odv46yibm5gf7evzoopmrrqr3q" style="color: black;">International Journal of Science and Research (IJSR)</a> </i> &nbsp;
Cellular Automata rules producing evolution type phenomena have been used for a wide range of applications. Various models have been designed and explored for different applications.  ...  Our present study was intended to identify the additive 2D Cellular Automata linear rules on the quality of pattern evolution and the periodic parallelism utilization.  ...  According to criteria of applying cellular automata rules to a group of data in any neighborhood, the cellular automata have been divided into two types: i) Uniform Cellular Automata ii) Non-Uniform Cellular  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.21275/20071710">doi:10.21275/20071710</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2h4yb5n7qrbnlety5w4oy74224">fatcat:2h4yb5n7qrbnlety5w4oy74224</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220302024802/https://www.ijsr.net/archive/v6i7/20071710.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0a/00/0a00fede5c4d177cfb4a02a287974769ec6a43ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.21275/20071710"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 127 of Automation and Remote Control Vol. 26, Issue 1 [page]

<span title="">1965</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
Here we will discuss two types of automata with a maximal number of components.  ...  It is natural to separate such automata into types determined by the order of the positions of the cones.  ... 
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Cone types and geodesic languages for lamplighter groups and Thompson's group F

Sean Cleary, Murray Elder, Jennifer Taback
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/h7qx4qsc2zf7hiupv27dke5fk4" style="color: black;">Journal of Algebra</a> </i> &nbsp;
many cone types with respect to that generating set.  ...  We show that the lamplighter groups L_n have infinitely many cone types, have no regular geodesic languages, and have 1-counter, context-free and counter geodesic languages with respect to certain generating  ...  Bartholdi and Šuniḱ [1] prove that all lamplighter groups L m are automata groups.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jalgebra.2005.11.016">doi:10.1016/j.jalgebra.2005.11.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ujmtwxghord3ngj5svqtxx4ebq">fatcat:ujmtwxghord3ngj5svqtxx4ebq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170926092335/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/3b5/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAyMTg2OTMwNTAwNjUwMg%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4e/60/4e6034fcd72c943ce19158afe628b34948c8f1df.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jalgebra.2005.11.016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Preface

Jan Baetens, Martin Kutrib
<span title="2020-09-12">2020</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6zolbg3dcjdt3edqtvzmiiuuim" style="color: black;">Natural Computing</a> </i> &nbsp;
Such cellular automata are necessarily left-closing, and they move at least as much information to the left as they move information to the right.  ...  It gives a decidable characterization of cellular automata which can be written as a single sweep of a bijective rule from left to right over an infinite tape.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11047-020-09804-4">doi:10.1007/s11047-020-09804-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hx2jzjpbhzatdjce77fmx72uce">fatcat:hx2jzjpbhzatdjce77fmx72uce</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201108162712/https://link.springer.com/content/pdf/10.1007/s11047-020-09804-4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ea/7f/ea7ff438fc49d5615b42953d1074a398891fb8e8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11047-020-09804-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 405 of Mathematical Reviews Vol. , Issue 93a [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The class of R-strongly connected automata in- cludes strongly connected, permutation, group type, state-indepen- dent and right simple type automata.  ...  Polynomial-time algorithms for testing strong isomorphism and computing the automorphism group of R-strongly connected automata are given.” 93a:68107 68Q75 Mubarakzyanov, R. G.  ... 
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Page 188 of Mathematical Reviews Vol. , Issue 2001A [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author of this paper characterizes the semigroups S for which every S-automaton is flat and investigates which type of S-automata are flat over a regular semigroup S.  ...  In this paper, the author shows that for an element x of a semigroup S, if x is right regular and regular, then the cyclic S-automaton S/p(x, x’) is flat, and then shows that if all cyclic automata over  ... 
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Page 705 of Mathematical Reviews Vol. 58, Issue 1 [page]

<span title="">1979</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For a certain type of automata algebra it is shown that the univer- sality problem is unsolvable.  ...  For this same type of automata alge- bra a completeness criterion, related to the existence of universal automata, is given. {For the entire collection see MR 54 #9826.} R. G.  ... 
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Page 1175 of Mathematical Reviews Vol. , Issue 85c [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Authors’ summary: “Necessary and sufficient conditions for a given automaton to be of left identity type, of identity type, of right group type, of group type, quasi-state-independent, and state-independent  ...  Pushdown tree automata (PDTAs) are introduced as generaliza- tions of the usual pushdown automata as well as of finite top- down tree automata.  ... 
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