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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: In this paper , it was shown that the deterministic membership problem for register automata is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton was fixed.
Abstract: The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of register automata. We draw the complete decidability/complexity landscape of the deterministic membership problem, in the setting of both register and timed automata. For register automata, we prove that the deterministic membership problem is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton is fixed. This is optimal: We show that in all the other cases the problem is undecidable, i.e., when either (1) the input nondeterministic automaton has two registers or more (even without epsilon transitions), or (2) it uses guessing, or (3) the number of registers of the output deterministic automaton is not fixed. The landscape for timed automata follows a similar pattern. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the output deterministic timed automaton is fixed. Again, this is optimal: We show that the problem in all the other cases is undecidable, i.e., when either (1) the input nondeterministic timed automaton has two clocks or more, or (2) it uses epsilon transitions, or (3) the number of clocks of the output deterministic automaton is not fixed.
TL;DR: In this paper, a sequence of one-dimensional deterministic binary cellular automata is used to determine the sign of a continuous function f(x) where ρ is the density of 1s in an arbitrarily given bit string of finite length provided f satisfies certain technical conditions.
Abstract: Given a continuous function f(x), suppose that the sign of f has only finitely many discontinuous points in the interval [0, 1]. We show how to use a sequence of one-dimensional deterministic binary cellular automata to determine the sign of f(ρ) where ρ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that f satisfies certain technical conditions.
17 Jun 1974
TL;DR: For the class of d-dimensional cellular automata, two general decision questions concerning the existence and recognizability of certain general "qualitative" properties of configurations in these automata are formulated.
Abstract: For the class of d-dimensional cellular automata, two general decision questions concerning the existence and recognizability of certain general "qualitative" properties of configurations in these automata are formulated. The problems can be stated as follows:
1.
Given a general property of configurations, does a configuration with this property exist in a cellular automaton ?
2.
Given a configuration in a cellular automaton, can we recognize certain (given) property of this configuration ?
TL;DR: It is shown that certain group properties are preserved in the semigroup of an automaton A of which r 2 (A) is restricted.
Abstract: This paper is a continuation of the study of the permutation rank of an automaton as was initiated in Smit [2]. The p 2 permutation r 2(A) of an automaton A is defined as the largest integer k such that (i) every subset of the state set of A consisting of k different states can be distinguished by an input; (ii) every input to A distinguishes k states of A. If x is an input string the expression “x distinguishes k states” means that k different states change to k different states which need not be the same as the original k states under the input x. The p 2 -permutation rank of a permutation automaton will always be equal to the number of states of the automaton. The semigroup of a permutation automaton is a group. It is shown that certain group properties are preserved in the semigroup of an automaton A of which r 2 (A) is restricted. The role of r 2 (A) in the semigroup of a strictly connected automaton is considered. As is in the case of Smit [2], it is shown that if r 2 (A) differs with only one from ...
TL;DR: In this article, a stochastic cellular automaton rule is considered which gives in two limiting cases Conway's "Life" and a Class 2 (according to Wolfram) cellular automata exhibiting domain structure.
Abstract: A stochastic cellular automaton rule is considered which gives in two limiting cases Conway’s “Life” and a Class 2 (according to Wolfram) cellular automaton exhibiting domain structure. By changing the difference between these two rules with concentrationc, a phase transition between phases of strongly different densities is found experimentally. A generalized inhomogeneous mean field approximation is proposed to account for the findings at least semi-quantitatively.