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Mobile automaton
About: Mobile automaton is a research topic. Over the lifetime, 2160 publications have been published within this topic receiving 63192 citations.
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TL;DR: The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages and it is suggested that such undecidability is common in these and other dynamical systems.
Abstract: Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata. The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be non-decreasing with time. The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. Many properties of these sets are then formally non-computable. It is suggested that such undecidability is common in these and other dynamical systems.
579 citations
24 Oct 1988
TL;DR: The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.
Abstract: Automata on infinite words were introduced by J.R. Buchi (1962) in order to give a decision procedure for S1S, the monadic second-order theory of one successor. D.E. Muller (1963) suggested deterministic omega -automata as a means of describing the behavior of nonstabilising circuits. R. McNaughton (1966) proved that classes of languages accepted by nondeterministic Buchi automata and by deterministic Muller automata are the same. His construction and its proof are quite complicated, and the blow-up of the construction is double exponential. The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case. This construction is essentially optimal. It can also be used to obtain an improved complementation construction for Buchi automata that is also optimal. Both constructions can be used to improve the complexity of decision procedures that use automata-theoretic techniques. >
551 citations
TL;DR: It is drawn that although the capacity for universal construction is a sufficient condition for self-reproduction, it is not a necessary condition, and a simple self- reproducing structure is exhibited which satisfies these new criteria.
526 citations
TL;DR: Is Nature, Underneath It All, a CA?
Abstract: * Introduction: Preliminary Musings * Formalism * Phenomenological Studies of Generic CA * Dynamical Systems Theory Approach * Analytic Approach * Cellular Automata and Language Theory * Probabilistic CA * Generalized Models * CA Models of Fluid Dynamics * Neural Networks * Artificial-Life * Is Nature, Underneath It All, a CA?
488 citations
TL;DR: A 1-dimensional cellular automaton which generates random sequences is discussed, and an efficient random sequence generator based on them is suggested.
472 citations