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Cellular automata over generalized Cayley graphs

PABLO ARRIGHI, SIMON MARTIEL, VINCENT NESME
2017 Mathematical Structures in Computer Science  
We propose a notion of graphs, which preserves or generalizes these features. Whereas Cayley graphs are very regular, generalized Cayley graphs are arbitrary, although of a bounded degree.  ...  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.  ...  For Cellular Automata over Cayley graphs a complete reference is [6] .  ... 
doi:10.1017/s0960129517000044 fatcat:rrsg6zukbverfjnxyqan2ekbdu

Generalized Cayley Graphs and Cellular Automata over them [article]

Pablo Arrighi, Simon Martiel, Vincent Nesme
2014 arXiv   pre-print
The obtained notion of Cellular Automata over generalized Cayley graphs is stable under composition and under inversion.  ...  KEYWORDS: Causal Graph Dynamics, Curtis-Hedlund-Lyndon, Dynamical networks, Boolean networks, Generative networks automata, Graph Automata, Graph rewriting automata, L-systems, parallel graph transformations  ...  For Cellular Automata over Cayley graphs a complete reference is [6] .  ... 
arXiv:1212.0027v2 fatcat:wtvvetwabfgbpbjwrsewvexteu

A simulation of cellular automata on hexagons by cellular automata on rings

Bruno Martin
2001 Theoretical Computer Science  
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

Preface

Ekaterina Fokina
2017 Mathematical Structures in Computer Science  
In Cellular Automata over Generalized Cayley Graphs Arrighi, Martiel and Nesme extend cellular automata theory to generalized Cayley graphs varying in time.  ...  They study basic computational properties of generalized Cayley graphs, and prove stability of the notion of Cellular Automata over generalized Cayley graphs under composability and taking inverses.  ... 
doi:10.1017/s0960129517000081 fatcat:34u577sexfhbblvx3kb4vsmn5m

A single-copy minimal-time simulation of a torus of automata by a ring of automata

Bruno Martin, Claudine Peyrat
2007 Discrete Applied Mathematics  
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).  ...  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] .  ...  For more examples of Cayley graphs which can serve to define cellular automata, one can refer to [3] .  ... 
doi:10.1016/j.dam.2007.05.019 fatcat:haj2uqepofeodld6j332zf2fb4

Page 5106 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
The author continues her study of cellular automata on Cayley graphs.  ...  automata on Cayley graphs.  ... 

The entropy and reversibility of cellular automata on Cayley tree [article]

Hasan Akin
2017 arXiv   pre-print
In this paper, we study linear cellular automata (CAs) on Cayley tree of order 2 over the field F_p (the set of prime numbers modulo p).  ...  We construct the rule matrix corresponding to finite cellular automata on Cayley tree.  ...  In this short paper, firstly we have defined linear cellular automata on Cayley tree of order 2.  ... 
arXiv:1211.7362v2 fatcat:xjpcb24yqfh65fq7z2zb3xwjgm

Cayley automata

Max Garzon
1993 Theoretical Computer Science  
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  ...  The purpose of this paper is to characterize group-theoretic properties recognizable by Cayley automata in the general case of n-generator Cayley graphs (groups) (n > 1).  ... 
doi:10.1016/0304-3975(93)90231-h fatcat:u7a37cfe5jdjll2ur3vpbkepyu

Amenable groups and cellular automata

Tullio G. Ceccherini-Silberstein, Antonio Machi, Fabio Scarabotti
1999 Annales de l'Institut Fourier  
Cellular automata on Cayley graphs. In this section we review some definitions and notations from [MaMi] . Let G be a finitely generated group and let A = {01,02,...  ...  -Generalize the game of life over other universes such as regular trees (these can be thought of as Cayley graphs of free groups, if the degree is even, or, more generally of Zs * ^2 * • • < * Zs (the  ... 
doi:10.5802/aif.1686 fatcat:wuihynitoncbdg3fmtgsmr6d6m

Free Quantum Field Theory from Quantum Cellular Automata

Alessandro Bisio, Giacomo Mauro D'Ariano, Paolo Perinotti, Alessandro Tosini
2015 Foundations of physics  
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.  ...  Given a group G and a set S of generators, the Cayley graph Γ(G, S) is defined as the colored directed graph having set of nodes G, set of edges {(g, gh); g ∈ G, h ∈ S}, and a color assigned to each generator  ... 
doi:10.1007/s10701-015-9934-1 fatcat:upkuxsdqoja23oorg7vqbsarrm

Preface

Jarkko Kari
2017 Natural Computing  
A general algorithm is provided based on the De Bruijn -graph representation of the cellular automaton.  ...  The fourth paper is by Ville Salo and Ilkka Törmä, and it is titled Independent Finite Automata on Cayley Graphs.  ... 
doi:10.1007/s11047-017-9615-4 fatcat:32c2ksyhtjcn7pcnsc25aptpaa

Groups, graphs, languages, automata, games and second-order monadic logic

Tullio Ceccherini-Silberstein, Michel Coornaert, Francesca Fiorenzi, Paul E. Schupp
2012 European journal of combinatorics (Print)  
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  ...  If follows from the decidability of the monadic second-order theory of Cayley graphs of context-free groups that the problem for cellular automata defined over virtually-free groups is decidable.  ...  Theorem 5.6) that the Surjectivity Problem for cellular automata defined over finitely generated virtually-free groups is decidable.  ... 
doi:10.1016/j.ejc.2012.03.010 fatcat:qebnsvnknvavtibb77kiga3hty

Page 4276 of Mathematical Reviews Vol. , Issue 95g [page]

1995 Mathematical Reviews  
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.  ... 

Intrinsic Universality of Causal Graph Dynamics

Simon Martiel, Bruno Martin
2013 Electronic Proceedings in Theoretical Computer Science  
Causal graph dynamics are transformations over graphs that capture two important symmetries of physics, namely causality and homogeneity.  ...  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.  ...  Introduction Causal Graph Dynamics have been introduced in [2, 5] as a generalization of cellular automata on arbitrary graphs.  ... 
doi:10.4204/eptcs.128.19 fatcat:nidpty7bcbhovbeupxz3qaumai

Page 433 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
In this paper the authors generalize the theorems of Moore and Myhill and prove that these theorems hold in the more general case of automata for which the universe is the Cayley graph of a finitely generated  ...  {For the entire collection see MR 94j:82002.} 95a:68084 68Q80 05C25 Machi, Antonio (I-ROME; Rome); Mignosi, Filippo (I-PLRM; Palermo) Garden of Eden configurations for cellular automata on Cayley graphs  ... 
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