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23
Universalities in cellular automata: a (short) survey
 Symposium on Cellular Automata Journées Automates Cellular (JAC 2008
, 2008
"... Abstract. This reading guide aims to provide the reader with an easy access to the study of universality in the field of cellular automata. To fulfill this goal, the approach taken here is organized in three parts: a detailed chronology of seminal papers, a discussion of the definition and main prop ..."
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Abstract. This reading guide aims to provide the reader with an easy access to the study of universality in the field of cellular automata. To fulfill this goal, the approach taken here is organized in three parts: a detailed chronology of seminal papers, a discussion of the definition and main properties of universal cellular automata, and a broad bibliography.
Bulking II: Classifications of Cellular Automata
, 2010
"... This paper is the second part of a serie of two papers dealing with bulking: a quasiorder on cellular automata comparing spacetime diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the p ..."
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Cited by 14 (3 self)
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This paper is the second part of a serie of two papers dealing with bulking: a quasiorder on cellular automata comparing spacetime diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we introduce 3 notions of simulation between cellular automata and study the quasiorder structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasiorders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools to classify cellular automata.
A Geometrical Hierarchy of Graphs via Cellular Automata
, 1998
"... Historically, cellular automata were defined on the lattices Z n , but the definition can be extended to bounded degree graphs. Given a notion of simulation between cellular automata defined on different structures (namely graphs of automata), we can deduce an order on graphs. In this paper, w ..."
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Cited by 13 (0 self)
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Historically, cellular automata were defined on the lattices Z n , but the definition can be extended to bounded degree graphs. Given a notion of simulation between cellular automata defined on different structures (namely graphs of automata), we can deduce an order on graphs. In this paper, we link this order to graph properties and explicit the order for most of the common graphs.
ON LOCAL SYMMETRIES AND UNIVERSALITY IN CELLULAR AUTOMATA
, 2009
"... Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. I ..."
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Cited by 10 (5 self)
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Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries. We extend results previously established for captive cellular automata in two significant ways. First, our results apply to wellknown families of CA (e.g. the family of outertotalistic CA containing the Game of Life) and, second, we obtain such density results with both increasing number of states and increasing neighbourhood. Moreover, thanks to universalitypreserving encodings, we show that the universality problem remains undecidable in some of those families.
An introduction to Cellular Automata
, 1998
"... We give basic definitions necessary to understand what are cellular automata, as well as to work with. Some efficient but sometimes problematic concepts as signal, simulation and universality, are pointed out. In particular, different notions of universality are put to light. ..."
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Cited by 10 (0 self)
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We give basic definitions necessary to understand what are cellular automata, as well as to work with. Some efficient but sometimes problematic concepts as signal, simulation and universality, are pointed out. In particular, different notions of universality are put to light.
Captive Cellular Automata
"... Abstract. We introduce a natural class of cellular automata characterised by a property of the local transition law without any assumption on the states set. We investigate some algebraic properties of the class and show that it contains intrinsically universal cellular automata. In addition we show ..."
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Cited by 6 (3 self)
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Abstract. We introduce a natural class of cellular automata characterised by a property of the local transition law without any assumption on the states set. We investigate some algebraic properties of the class and show that it contains intrinsically universal cellular automata. In addition we show that Rice’s theorem for limit sets is no longer true for that class, although infinitely many properties of limit sets are still undecidable. Cellular automata (ca for short) are discrete dynamical systems capable of producing a wide class of different behaviours. They consist of a large collection of simple identical components (the cells) with uniform local interactions. As such they provide an idealistic model to study complex systems observed in nature. Despite the simplicity of the model, most of the richness of behaviours they exhibit is still to be understood. Moreover, many interesting and natural properties are undecidable. To that extent it is meaningful to consider classes of ca obtained by structural assumptions on the local transition law with the
Towards a Rice theorem on traces of cellular automata
 In 32 nd Conference on Mathematical Foundations of Computer Science (MFCS’07
, 2007
"... Abstract. The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a spacetime diagram. We prove the undecidability of a rather large class of problems over trace subshifts of cellular automata. ..."
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Cited by 6 (4 self)
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Abstract. The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a spacetime diagram. We prove the undecidability of a rather large class of problems over trace subshifts of cellular automata.
On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures
"... Abstract. We study the notion of limit sets of cellular automata associated with probability measures (µlimit sets). This notion was introduced by P. K˚urka and A. Maass in [1]. It is a refinement of the classical notion of ωlimit sets dealing with the typical long term behavior of cellular automa ..."
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Cited by 5 (2 self)
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Abstract. We study the notion of limit sets of cellular automata associated with probability measures (µlimit sets). This notion was introduced by P. K˚urka and A. Maass in [1]. It is a refinement of the classical notion of ωlimit sets dealing with the typical long term behavior of cellular automata. It focuses on the words whose probability of appearance does not tend to 0 as time tends to infinity (the persistent words). In this paper, we give a characterization of the persistent language for non sensitive cellular automata associated with Bernoulli measures. We also study the computational complexity of these languages. We show that the persistent language can be nonrecursive. But our main result is that the set of quasinilpotent cellular automata (those with a single configuration in their µlimit set) is neither recursively enumerable nor corecursively enumerable. 1