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Showing papers on "Continuous automaton published in 1992"


Book ChapterDOI
06 Apr 1992
TL;DR: Four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states are given and it is shown that one can effectively decide whether a given rational (or regular) language can be accepted by the automaton.
Abstract: A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be accepted by a reversible automaton. The first characterization gives a description of the subsets of the free group accepted by a reversible automaton that is somewhat reminiscent of Kleene's theorem. The second characterization is more combinatorial in nature. The decidability follows from the third — algebraic -characterization. The last characterization relates reversible automata to the profinite group topology of the free monoid.

108 citations


Journal ArticleDOI
TL;DR: In this article, a cellular automation model of excitable media with improved treatments of diffusion and wave propagation, and slow dynamics of the recovery variable is introduced. But the model is computationally efficient and faithful to the underlying partial differential equations.

42 citations


Journal ArticleDOI
TL;DR: In this article, a certain class of cellular automata in 1 space + 1 time dimension is shown to be closely related to quantum field theories containing Dirac fermions, which can be studied analytically, while the introduction of Dirac mass requires numerical simulations.

38 citations


Journal ArticleDOI
TL;DR: This paper demonstrates that the one-dimensional three-color cyclic cellular automaton clusters, and the mean cluster size, as a function of time t, is asymptotic to ct1/2, where c is an explicitly calculable constant.
Abstract: cyclic cellular automaton. The author has previously shown that this process fluctuates, meaning that each lattice site changes color infinitely often, so that there is no "final state" for the system. The focus of the current work is on the clustering properties of this system. This paper demonstrates that the one-dimensional three-color cyclic cellular automaton clusters, and the mean cluster size, as a function of time t, is asymptotic to ct1/2, where c is an explicitly calculable constant. The method of proof also allows us to compute asymptotic estimates of the mean interparticle distance for a one-dimensional system of particles which undergo deterministic motion and which annihilate upon collision. No clustering results are known about the four-color process, but evidence is presented to suggest that the mean cluster size of such systems grows at a rate different from t1/2.

32 citations


Journal ArticleDOI
TL;DR: The simulations show that the average transient time Tave increases algebraically with system size N, Tave∼Nα, with α≈1.08, and that the density of propagating objects (gliders) decays with time as ngl∼-γ with γ≈0.64.

19 citations


Journal ArticleDOI
TL;DR: A new ergodic discretized learning automaton which is epsilon- optimal is introduced which utilizes a new estimator learning algorithm which is based on the recent history of the environmental responses and is able to operate in nonstationary stochastic environments.

14 citations


Journal ArticleDOI
TL;DR: A multistate cellular automaton model for computational simulation of reaction-diffusion processes at the microscopic level is presented and the microscopic dynamics is fully identified with the corresponding macroscopic reaction- Diffusion laws.
Abstract: A multistate cellular automaton model for computational simulation of reaction-diffusion processes at the microscopic level is presented. Diffusion is introduced through a standard stochastic scheme. On the other hand, the reaction dynamics, which applies to generic chemical reactions, consists of a deterministic algorithm driven by a discrete mapping. By means of a proper average on the states of the cellular automaton, the microscopic dynamics is fully identified with the corresponding macroscopic reaction-diffusion laws.

13 citations


Journal ArticleDOI
TL;DR: In this paper, an energy-conserved cellular automaton is proposed, which is a generalization of the Park, Steiglitz and Thurston model and contains richer solitonic phenomena.
Abstract: An energy-conserved soliton cellular automaton is proposed. It is a generalization of the Park, Steiglitz and Thurston model (1986), and is shown to contain richer solitonic phenomena. A systematic comparison of their collision statistics is also given.

10 citations


Journal ArticleDOI
01 Feb 1992
TL;DR: The main results show that there are rather strong constraints on the collection of attractors for any restricted cellular automaton.
Abstract: The goal of this note is to extend previous results about the dynamics of cellular automata to «restricted cellular automata». Roughly speaking, a cellular automaton is a rule that updates a configuration of «states» that are arranged along the integer lattice in R. In applications one often thinks of one of these states as «bank» or «quiescent», while the other «active» states evolve against a quiescent background. Often the physically relevant configurations are those with only a finite number of active states. If X 0 is the set of all such states, and if a cellular automaton maps X 0 to X 0 , then its restriction to X 0 is a restricted cellular automaton. The main results show that there are rather strong constraints on the collection of attractors for any restricted cellular automaton. These constraints parallel those described in [H1] for the unrestricted case

8 citations


Proceedings ArticleDOI
14 Oct 1992
TL;DR: General methods of designing a discrete-time cellular neural network implementing an arbitrary Boolean function defined on the r-neighborhood are described, achieved by operating the network with time-invariant templates as a cellular automaton that processes only binary inputs.
Abstract: General methods of designing a discrete-time cellular neural network implementing an arbitrary Boolean function defined on the r-neighborhood are described. This is achieved by operating the network with time-invariant templates as a cellular automaton that processes only binary inputs. These methods are suitable for solving local tasks. As an example, testing minimal distances is discussed. >

8 citations


Book ChapterDOI
24 Aug 1992
TL;DR: This paper improves the complexities in time and in space of the intrinsically universal cellular automaton of J. Albert and K. Culik, and gives notions of what a parallel computation is for one dimensional cellular automata.
Abstract: In this paper we present an intrinsically universal one dimensional cellular automaton. By intrinsic, we mean that it does not simulate a universal Turing machine, which is a well-known result, but it simulates any other cellular automaton on any input. We thus improve the complexities in time and in space of the intrinsically universal cellular automaton of J. Albert and K. Culik, and we give notions of what a parallel computation is for one dimensional cellular automata.

Journal ArticleDOI
TL;DR: This work associates to each copy of a Q2R an equivalent automaton M2R, which, with the Margoluos neighborhood, exhibits the local changes of the Q1R energy, and generalizes the dynamics by upgrading M1R according to four partitions of the lattice.
Abstract: In this work we study the computing capabilities as well as some dynamical properties of an automaton called M4R. This automaton corresponds to the mixing of the energy profiles of two independent copies of the Q2R automaton with frustrations. We associate to each copy of a Q2R an equivalent automaton M2R, which, with the Margoluos neighborhood, exhibits the local changes of the Q2R energy.1 By doing so we generalize the dynamics by upgrading M2R according to four partitions of the lattice. This new dynamics — called M4R — is based on a local rule which corresponds to the local energy change of two independent copies of Q2R. The M4R model is reversible and conservative (magnetization is constant in time) and it has properties of a discrete billiard (as some of the hydrodynamics discrete versions of Navier-Stokes models). Moreover, this automaton has powerful computing capabilities. In fact, by using some special configurations of M4R, we exhibit universal gates and register that allow us to code any algorithm.

Proceedings ArticleDOI
TL;DR: In this paper, a stochastic, linear, S-model automaton model is proposed for distributed adaptive routing in packet-switched datagram networks and the performance of two automata-based adaptive routing algorithms is compared.
Abstract: Large computer networks with dynamic links present special problems in adaptive routing. If the rate of change in the network links is fairly rapid and the changes are nonperiodic, then obtaining the optimal solution for adaptive routing becomes complex and expensive. In addition to the academic value of the solution, the growth of computer networks gives the problem practical importance. Learning automata is logical approach to the above problem. With the right parameter values, learning automata can converge arbitrarily close to the solution for a given network topology and set of conditions. The adaptability of automata reduces the depth of analysis needed for network behavior; the survivability and robustness of the network is also enhanced. Finally, each automaton behaves independently, making automata ideal for distributed decision-making, and minimizing the need for inter-node communication. Previous work on automata and network routing do not address how changes in network parameter values affect the performance of automata-based adaptive routing. Such knowledge is essential if we are to determine the suitability of an automata-based routing algorithm for a given network. Our paper focuses on this question and shows that in packet- switched datagram networks, relationships do indeed exist between network parameters and the performance of distributed adaptive routing algorithms. Additionally, our paper compares the performance and behavior of several types of learning automata, as well as changes in automata behavior over a range of reward and penalty values. Finally, the performance of two automata-based adaptive routing algorithms is compared. Our automaton model is a stochastic, linear, S-model automaton. In other words, the automaton's matrix of action probabilities changes as a result of performance feedback which it receives from the environment, the response to environment feedback is linear, and finally, the feedback it receives from the environment is over a continuous interval.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Book ChapterDOI
24 Aug 1992
TL;DR: This paper associates to every one-dimensional cellular automaton a finitely presented semigroup that is shown to have solvable word problem if and only if the common descendant problem is solvable for the cellular Automaton.
Abstract: We associate to every one-dimensional cellular automaton a finitely presented semigroup. This semigroup is shown to have solvable word problem if and only if the common descendant problem is solvable for the cellular automaton. Connections with Culik and Yu's classification of cellular automata are investigated.

Journal ArticleDOI
TL;DR: A maximum-entropy frequency analysis of the occupation-density time series for a recently proposed totalistic cellular automaton rule in five dimensions is performed and the possible phenomenology of the model is discussed.
Abstract: We perform a maximum-entropy frequency analysis of the occupation-density time series for a recently proposed totalistic cellular automaton rule in five dimensions. This new information complements partial knowledge coming from winding number measurements. We discuss the possible phenomenology of the model in terms of our findings.

01 Sep 1992
TL;DR: In this paper, an optical incoherent implementation of a general and programmable cellular automaton is reported, which is based on an incoherent multiple-imaging system and electronic nonlinear circuits.
Abstract: Abstract An optical incoherent implementation of a general and programmable cellular automaton is reported. The implementation is based on an incoherent multiple-imaging system and electronic nonlinear circuits. All of 256 distinct local rules of a 1D elementary cellular automaton are achieved by simply specifying the different transparencies of a spatial light modulator (SLM) mask. The complex cellular automata can be synthesized based on the optical system. Simulations and experimental results are also given.

Journal Article
TL;DR: It is shown that under this metric, for cert ain regular langu ages, the set of rules under which the language is invariant contains no interior, and its compleme nt containsno interior.
Abstract: Procedures are given for det ermining regul ar language invariance under on e-dimensi on al cellular auto maton rul es. A met ric is defined for t he space of all one-dimensional cellular automato n rules over a given alphabet :E . It is shown that under this metric, for cert ain regular langu ages , the set of rules under which the language is invariant contains no interior, and its compleme nt contains no interior. Ch ar act eristics of surjective rules (rules under which t he regular langu age :E* is invariant) ar e also explored. Examples ar e given of a sequence of rul es for which the limit lan gu age of the limit rul e is not invari ant under any rul e in the sequence. Numerical experime nts indicate that t hese rules do indeed display discont inuous behavior.