Topic
Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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TL;DR: It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications (CA_{1-bit}) using 34 internal states and 71 transition rules.
Abstract: It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications (CA_{1-bit}). The algorithm presented is based on the classical sieve of Eratosthenes, and its implementation will be made on a CA_{1-bit} using 34 internal states and 71 transition rules.
35 citations
08 Mar 2003
TL;DR: A classification of cellular automata based on the Turing degree of the orbits of the automaton is studied, finding that the difficulty of determining the membership of a cellular automaton in any one of these classes is characterized in the arithmetical hierarchy.
Abstract: We study a classification of cellular automata based on the Turing degree of the orbits of the automaton. The difficulty of determining the membership of a cellular automaton in any one of these classes is characterized in the arithmetical hierarchy.
35 citations
08 Jul 2002
TL;DR: This paper gives in this paper a method to compute a reversible automaton from the minimal automaton of a reversible language that contains an equivalent automaton which is quasi-reversible.
Abstract: Reversible languages occur in many different domains Although the decision for the membership of reversible languages was solved in 1992 by Pin, an effective construction of a reversible automaton for a reversible language was still unknown We give in this paper a method to compute a reversible automaton from the minimal automaton of a reversible language With this intention, we use the universal automaton of the language that can be obtained from the minimal automaton and that contains an equivalent automaton which is quasi-reversible This quasi-reversible automaton has nearly the same properties as a reversible one and can easily be turned into a reversible automaton
35 citations
TL;DR: A complete answer to the question whether a double sequence that is generated by a one-dimensional linear cellular automaton, and whose states are integers modulo m, is k -automatic or not is given.
35 citations
TL;DR: A one-dimensional solution that is based on multiplying numbers by a suitable constant is described and the automaton to multiply by constant 3/2 is shown to be related to some difficult open questions in number theory.
34 citations