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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: It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic, in simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics.
Abstract: We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from chemotaxis. Here we study a rather simple situation, namely the evacuation from a large room with one or two doors. It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic. We find a non-monotonic dependence of the evacuation times on the coupling constants. These times depend on the strength of the herding behaviour, with minimal evacuation times for some intermediate values of the couplings, i.e., a proper combination of herding and use of knowledge about the shortest way to the exit.
858 citations
TL;DR: The question of whether there is an automaton with n states which agrees with a finite set D of data is shown to be NP-complete, although identification-in-the-limit of finite automata is possible in polynomial time as a function of the size of D.
Abstract: The question of whether there is an automaton with n states which agrees with a finite set D of data is shown to be NP-complete, although identification-in-the-limit of finite automata is possible in polynomial time as a function of the size of D. Necessary and sufficient conditions are given for D to be realizable by an automaton whose states are reachable from the initial state by a given set T of input strings. Although this question is also NP-complete, these conditions suggest heuristic approaches. Even if a solution to this problem were available, it is shown that finding a minimal set T does not necessarily give the smallest possible T.
819 citations
TL;DR: In this paper, it was shown that there is no nontrivial, homogeneous, local, unitary, scalar cellular automata in one dimension, and that the homogeneity condition can be overcome by a quantum cellular automaton with exactly unitary partitioning.
Abstract: A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.
730 citations
TL;DR: Two apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata, and it is this problem to which the remainder of this paper will address itself.
Abstract: Bfichi (1962) has given a decision procedure for a system of logic known as \" the Sequential Calculus,\" by showing that each well formed formula of the system is equivalent to a fornmla that, roughly speaking, says something about the infinite input history of a finite automaton. In so doing he managed to answer an open question that was of concern to pure logicians, some of whom had no interest in the theory of automata. Muller (1963) came upon quite similar concepts in studying a problem in asynchronous switching theory. The problem was to describe the behavior of an asynchronous circuit tha t does not reach any stability condition when starting from a certain state and subject to a certain input condition. Many different things can happen, since there is no control over how fast various parts of the circuit react with respect to each other. Since at no time during the presence of that input condition will the circuit reach a terminal condition, it will be possible to describe the total set of possibilities in an ideal fashioll only if an infinite amount of time is assumed for tha t input condition. Neither Biichi's Sequential Calculus nor ~Iuller's problem of asynchronous circuitry will be described further here. I t is interesting tha t two such apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata. I t is this problem to which the remainder of this paper will address itself. I t will be recalled that a well known basic theorem in the theory of
553 citations
01 Apr 1958
TL;DR: For a finite commutative ring with unit the authors determine which linear transformations M: RN—+RN can be realized by finite automata.
Abstract: Let R be a nonempty set, let N consist of all non-negative rational integers, and denote by RN the set of all functions on N to R. If R is a ring, a map M: R"—>P^ is linear if M(rxfx+r2f2)=rx(Mfx) +r2(Mf2) for rx, r2 in R, fx, f2 in RN. For a finite commutative ring with unit we determine which linear transformations M: RN—+RN can be realized by finite automata. More precisely, let A, B he finite nonempty sets. A map M: AN—>BN is an automaton transformation if there exists a finite set Q, maps Mq: A X£>—><2, Mb: A XQ-*B, elements h in B, q in Q such that corresponding to each/ in AN there exists an h in QN satisfying
526 citations