Invertible Linear Cellular Automata overZm
Giovanni Manzini,Luciano Margara +1 more
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TLDR
In this paper, an explicit and efficiently computable formula for the inverse of D-dimensional linear cellular automata over Zm(D?1, m?2) is given.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1998-02-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Invertible matrix & Cellular automaton.read more
Citations
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Journal ArticleDOI
Theory of cellular automata: a survey
TL;DR: The main goal is to provide a tutorial of CA theory to researchers in other branches of natural computing, to give a compact collection of known results with references to their proofs, and to suggest some open problems.
Journal ArticleDOI
A brief history of cellular automata
TL;DR: A history of cellular automata from their beginnings with von Neumann to the present day is traced, mainly on topics closer to computer science and mathematics rather than physics, biology or other applications.
Book ChapterDOI
Reversible cellular automata
TL;DR: This paper is a short survey of research on reversible cellular automata over the past fourty plus years and discusses the classic results by Hedlund, Moore and Myhill that relate injectivity, surjectivity and reversibility with each other.
Journal ArticleDOI
The dynamics of conjunctive and disjunctive Boolean network models.
TL;DR: A sharp lower bound and an upper bound on the number of limit cycles of a given length are provided, in terms of properties of the partially ordered set of strongly connected components.
Journal ArticleDOI
On computing the entropy of cellular automata
TL;DR: A closed formula is proved for the topological entropy of D-dimensional (D?1) linear cellular automata over the ring Zm(m?2) and an algorithm is provided for computing the topology entropy of positively expansive Cellular automata.
References
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Journal ArticleDOI
Endomorphisms and automorphisms of the shift dynamical system
TL;DR: It is shown that closed subset of X(SQ which is invariant under a defines a subdynamical system, and that these mappings, composed with powers of the shift, constitute the entire class of continuous transformations which commute with the shift.
Journal ArticleDOI
Invertible cellular automata: a review
Tommaso Toffoli,Norman Margolus +1 more
TL;DR: In this article, a unified presentation of the subject and its relevance to computer science and mathematical physics is presented. But this work is restricted to the theory of invertible cellular automata.
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Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Serafino Amoroso,Yale N. Patt +1 more
TL;DR: After demonstrating the existence of nontrivial information Jossless parallel maps on one-dimensional iterative array configurations, algorithms are presented for deciding the injectivity or surjectivity of the global maps given their defining local maps.
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Reversibility and surjectivity problems of cellular automata
TL;DR: It is shown that the reversibility problem is undecidable in case of two-dimensional CA, and it is proved that the corresponding surjectivity problem-the problem of deciding if the global function is surjective-is Undecidable for two- dimensional CA.