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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01 Nov 2016
TL;DR: This paper focuses on the case the authors call finite NCCA when states are non-negative integers, and the total sum is finite, and constructed a radius 1 universal FNCCA by simulating register machines with two registers.
Abstract: A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of particle-based modeling of the physical conservation law of mass. In this paper we focus on the case we call finite NCCA when states are non-negative integers, and the total sum is finite. In spite of the strong constraint, we constructed a radius 1 universal FNCCA by simulating register machines with two registers. We also consider the particle complexity in the case of large (but finite) radius, and constructed a universal FNCCA with only five particles.
5 citations
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Abstract: In this paper, following the way opened by a previous paper deposited on arXiv, we give an upper bound to the number of states for a hyperbolic cellular automaton in the pentagrid. Indeed, we prove that there is a hyperbolic cellular automaton which is rotation invariant and whose halting problem is undecidable and which has 9~states.
5 citations
TL;DR: A difference equation is constructed which preserves any time evolution pattern of the rule 90 Elementary cellular automaton and it is demonstrated that such difference equations can be obtained for any elementary cellular automata.
Abstract: We construct a difference equation which preserves any time evolution pattern of the rule 90 elementary cellular automaton. We also demonstrate that such difference equations can be obtained for any elementary cellular automata.
5 citations
07 Jul 2009
TL;DR: Any acyclic n -state automaton can be turned into an extended expression of size O (n) , and new regular operators are defined, called multi-tilde-bars, allowing us to simultaneously apply a multi-Tilde operator and aMulti-bar one to a list of expressions.
Abstract: A regular expression with n occurrences of symbol can be converted into an equivalent automaton with n + 1 states, the so-called Glushkov automaton of the expression Conversely, it is possible to decide whether a given (n + 1)-state automaton is a Glushkov one and, if so, to convert it back to an equivalent regular expression of size n Our goal is to extend the class of automata for which such a linear retranslation is possible We define new regular operators, called multi-tilde-bars, allowing us to simultaneously apply a multi-tilde operator and a multi-bar one to a list of expressions The main result is that any acyclic n -state automaton can be turned into an extended expression of size O (n )
5 citations
TL;DR: The connection between this isomorphism and the inertial relation on the state-space is explored, leading to more general statements, including a pseudo-homogeneous automaton is pseudo-isomorphic to a group-quotient automaton.
Abstract: Every cyclic automaton is isomorphic to a semi-group quotient automaton, while for a homogeneous automaton the semi-group may be replaced by a group. The connection between this isomorphism and the inertial relation on the state-space is explored, leading to more general statements. For example, a pseudo-homogeneous automaton is pseudo-isomorphic to a group-quotient automaton.
5 citations