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It is not possible to define one-way triangular cellular automata on a one-way Cayley graph. Proof. ... In order to define one-way cellular automata, we first define one-way Cayley graphs. Definition 3.8. Let r be the Cayley graph of the group G. ...doi:10.1016/0304-3975(94)90236-4 fatcat:mqzgm5o7urbcbgpvhvt2tutsju
We consider cellular automata on Cayley graphs and compare their computational powers according to the architecture on which t h e y work. ... Cayley graph of one of these groups can be uniformally simulated by a cellular automaton on the Cayley graph of the other one. ... We h a ve g i v en a su cient condition for converse simulations between cellular automata on Cayley graph. Can any su cient and necessary condition be given? ...doi:10.1016/s0304-3975(97)00213-2 fatcat:7f5i2z5dljajdofytirsn4c3xa
Lecture Notes in Computer Science
We consider cellular automata on Cayley graphs and compare their computational powers according to the architecture on which t h e y work. ... Cayley graph of one of these groups can be uniformally simulated by a cellular automaton on the Cayley graph of the other one. ... We h a ve g i v en a su cient condition for converse simulations between cellular automata on Cayley graph. Can any su cient and necessary condition be given? ...doi:10.1007/3-540-59175-3_112 fatcat:m6i4ytk5hjfuvbkjkobjf5ytre
We generalize this problem on Cayley graphs. ... The ÿring squad synchronization problem (FSSP for short) has been intensively studied in the one-dimensional space. The problem consists in the synchronization of a segment of automata. ... Cellular automata on Cayley graphs Let us ÿrst recall the deÿnitions of Cayley graphs and of cellular automata on Cayley graphs. ...doi:10.1016/s0304-3975(00)00160-2 fatcat:a5zhwernd5cnfakwfzmmagkjym
We consider cellular automata on Cayley graphs and compare their computational power according to their topology. ... We prove that cellular automata deÿned over a hexagonal grid can be simulated by cellular automata over a ring. ... Cellular automata on Cayley graphs Let us recall some deÿnitions. ...doi:10.1016/s0304-3975(00)00244-9 fatcat:j5c5td5tvngnjfakqnkmepagza
We consider cellular automata on Cayley graphs and we simulate the behavior of a torus of n × m automata (nodes) by a ring of n · m automata (cells). ... When the condition on n and m is not fulfilled one can use the previous algorithm. ... Definitions and notation Cellular automata and Cayley graphs Cellular automata on Cayley graphs have been introduced to prove a generalization of the Moore and Myhill theorem [1, 7] . ...doi:10.1016/j.dam.2007.05.019 fatcat:haj2uqepofeodld6j332zf2fb4
The obtained notion of Cellular Automata over generalized Cayley graphs is stable under composition and under inversion. ... Moreover, it is well-known that cellular automata can be characterized as the set of translation-invariant continuous functions for a distance on the set of configurations that makes it a compact metric ... For Cellular Automata over Cayley graphs a complete reference is  . ...arXiv:1212.0027v2 fatcat:wtvvetwabfgbpbjwrsewvexteu
We extend cellular automata theory to these arbitrary, bounded degree, time-varying graphs. The obtained notion of cellular automata is stable under composition and under inversion. ... from grids to Cayley graphs. ... For Cellular Automata over Cayley graphs a complete reference is  . ...doi:10.1017/s0960129517000044 fatcat:rrsg6zukbverfjnxyqan2ekbdu
The notion of one-way cellular automaton is generalized to cellular automata with structures specified by Cayley graphs. ... Do Long Van (VN-HMI; Hanoi) 95g:68080 68Q80 Roka, Zsuzsanna (F-ENSLY-LI; Lyon) One-way cellular automata on Cayley graphs. (English summary) Theoret. Comput. Sci. 132 (1994), no. 1-2, 259-290. ...
The fourth paper is by Ville Salo and Ilkka Törmä, and it is titled Independent Finite Automata on Cayley Graphs. ... The second paper, by Martin Kutrib, Andreas Malcher and Matthias Wendlandt, is titled Shrinking One-Way Cellular Automata. ...doi:10.1007/s11047-017-9615-4 fatcat:32c2ksyhtjcn7pcnsc25aptpaa
We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. ... The paper presents a synthetic derivation of the automata theory, showing how from the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. ... Keeping locality and homogeneity one could study automata defined on arbitrary Cayley graphs, relaxing the hypothesis of isotropy and Abelianity. ...doi:10.1007/s10701-015-9934-1 fatcat:upkuxsdqoja23oorg7vqbsarrm
Also, the definite advantage of nondeterminism is established for Cayley automata on input graphs with at least two generators. ... Cayley graph languages accepted by halting Cayley automata are syntactically characterized by quantifierfree formulas in the first-order theory of groups with parameters, the generators of the input Cayley ... might use the stronger result of decidability of emptiness of one-way stack automata  (also see 171) in order to prove a slightly stronger similar result for nondeterministic one-pebble automata. ...doi:10.1016/0304-3975(93)90231-h fatcat:u7a37cfe5jdjll2ur3vpbkepyu
In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order ... Also, we wish to warmly thank Maurice Margenstern for providing fruitful information on the Domino Problem on the hyperbolic plane. ... Acknowledgements We would like to express our deepest gratitude to Tony Martin for a very interesting and stimulating conversation on infinite games of perfect information and the Borel determinacy. ...doi:10.1016/j.ejc.2012.03.010 fatcat:qebnsvnknvavtibb77kiga3hty
diagrams, phase space), various types of cellular automata (totalistic, CA on Cayley graphs) and signal processes and computational powers. ... Culik, II, Decision problems on global cellular automata (331-344); E. Rémila, An introduction to automata on graphs (345-363). ...
They can be equivalently defined as continuous and translation invariant transformations or functions induced by a local rule applied simultaneously on every vertex of the graph. ... Causal graph dynamics are transformations over graphs that capture two important symmetries of physics, namely causality and homogeneity. ... Like cellular automata, they can be defined in two different ways. ...doi:10.4204/eptcs.128.19 fatcat:nidpty7bcbhovbeupxz3qaumai
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