Showing papers on "Continuous automaton published in 1999"
06 Jul 1999
TL;DR: The experimental results show that the state-of-the-art algorithm for obtaining an automaton from a linear temporal logic formula outperforms the previous one, with respect to both the size of the generated automata and computation time.
Abstract: We improve the state-of-the-art algorithm for obtaining an automaton from a linear temporal logic formula. The automaton is intended to be used for model checking, as well as for satisfiability checking. Therefore, the algorithm is mainly concerned with keeping the automaton as small as possible. The experimental results show that our algorithm outperforms the previous one, with respect to both the size of the generated automata and computation time. The testing is performed following a newly developed methodology based on the use of randomly generated formulas.
219 citations
TL;DR: In this paper, a soliton cellular automaton, which represents movement of a finite number of balls in an array of boxes, is investigated, and its dynamics is described by an ultra-discrete equation obtained from an extended Toda molecule equation.
Abstract: A soliton cellular automaton, which represents movement of a finite number of balls in an array of boxes, is investigated. Its dynamics is described by an ultra-discrete equation obtained from an extended Toda molecule equation. The rules for soliton interactions and factorization property of the scattering matrices (Yang-Baxter relation) are proved by means of inverse ultra-discretization. The conserved quantities are also presented and used for another proof of the solitonical nature.
102 citations
Journal Article•
TL;DR: It is shown here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable, implying the decidability of model checking for some properties which cannot be expressed in timed temporal logics.
Abstract: A configuration of a timed automaton is given by a control state and finitely many clock (real) values. We show here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable. This result implies the decidability of model checking for some properties which cannot be expressed in timed temporal logics and provide with alternative proofs of some known decidable properties. Our proof relies on two intermediate results: 1. Every timed automaton can be effectively emulated by a timed automaton which does not contain nested loops. 2. The binary reachability relation for counter automata without nested loops (called here flat automata) is expressible in the additive theory of integers (resp. real numbers). The second result can be derived from [10].
85 citations
24 Aug 1999
TL;DR: In this paper, it was shown that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable.
Abstract: A configuration of a timed automaton is given by a control state and finitely many clock (real) values. We show here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable. This result implies the decidability of model checking for some properties which cannot be expressed in timed temporal logics and provide with alternative proofs of some known decidable properties. Our proof relies on two intermediate results: 1. Every timed automaton can be effectively emulated by a timed automaton which does not contain nested loops. 2. The binary reachability relation for counter automata without nested loops (called here flat automata) is expressible in the additive theory of integers (resp. real numbers). The second result can be derived from [10].
84 citations
TL;DR: In this paper, it was shown that if φ is a closing map, then the configurations which are both spatially and temporally periodic are dense, and that the results are special cases of results for shifts of finite type.
58 citations
28 Mar 1999
TL;DR: A new definition of strong topological chaos for discrete time dynamical systems which fulfills the informal intuition of chaotic behavior that everyone has in mind is proposed and it is proved that under this new definition, the bi-infinite shift is no more chaotic.
Abstract: The shift (bi-infinite) cellular automaton is a chaotic dynamical system according to all the definitions of deterministic chaos given for discrete time dynamical systems (e.g., those given by Devaney [6] and by Knudsen [10]). The main motivation to this fact is that the temporal evolution of the shift cellular automaton under finite description of the initial state is unpredictable . Even tough rigorously proved according to widely accepted formal definitions of chaos, the chaoticity of the shift cellular automaton remains quite counterintuitive and in some sense unsatisfactory. The space-time patterns generated by a shift cellular automaton do not correspond to those one expects from a chaotic process. In this paper we propose a new definition of strong topological chaos for discrete time dynamical systems which fulfills the informal intuition of chaotic behavior that everyone has in mind. We prove that under this new definition, the bi-infinite shift is no more chaotic. Moreover, we put into relation the new definition of chaos and those given by Devaney and Knudsen. In the second part of this paper we focus our attention on the class of additive cellular automata (those based on additive local rules) and we prove that essential transformations [2] preserve the new definition of chaos given in the first part of this paper and many other aspects of their global qualitative dynamics.
37 citations
07 Dec 1999
TL;DR: It is shown that an automaton, with the nodes corresponding to distinct behaviors, may exhibit an infinite number of discrete transitions in finite time (a so called Zeno hybrid automaton), which can be dealt with by a regularization procedure, involving adding extra nodes to the automaton.
Abstract: Investigates how to model a behavior based control system for mobile robots as a hybrid automaton We show that an automaton, with the nodes corresponding to distinct behaviors, may exhibit an infinite number of discrete transitions in finite time (a so called Zeno hybrid automaton) This can be dealt with by a regularization procedure, involving adding extra nodes to the automaton which gives a system with similar performance as a fused behavior based system The performance aspect is also verified experimentally
36 citations
Metz1
TL;DR: It is shown that, if there exists a homomorphism with a finite kernel from a group into another one such that the image of the first group has a finite index in the second one, then every cellular automaton on the Cayley graph of one of these groups can be uniformly simulated by a cellular automata on the Bayesian graph of the other one.
32 citations
TL;DR: The aim of this work is to provide a method for accelerating the execution of algorithms based on Cellular Automata (Cellular Automata algorithms) and to build a bridge between cellular Automata as models for physical systems and processes and Cellular Automaton as a VLSI architecture.
17 citations
TL;DR: Here, it is proved that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two Cellular automaton rules in succession.
Abstract: Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states 0,1,…,n-1; can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two cellular automaton rules in succession.
14 citations
Patent•
14 Jul 1999
TL;DR: In this paper, a cellular automata neural network method for process modeling of film-substrate interactions was proposed, where variable rules describe a state change algorithm for atoms or other objects near a substrate.
Abstract: A cellular automata neural network method for process modeling of film-substrate interactions utilizes a cellular automaton system having variable rules for each cell. The variable rules describe a state change algorithm for atoms or other objects near a substrate. The state change algorithm is used to create a training set of solutions for training a neural network. The cellular automaton system is run to model the film-substrate interactions with the neural network providing the state change solutions in place of the more computationally complex state change algorithm to achieve real-time or near real-time simulations.
11 Jul 1999
TL;DR: The investigation of the computational power of randomized computations is one of the central tasks of complexity and algorithm theory and there is no nontrivial result relating the power of determinism, Las Vegas and nondeterminism for two-way finite automata.
Abstract: The investigation of the computational power of randomized computations is one of the central tasks of complexity and algorithm theory. This paper continues in the comparison of the computational power of Las Vegas computations with the computational power of deterministic and nondeterministic ones. While for one-way finite automata the power of different computational modes was successfully determined one does not have any nontrivial result relating the power of determinism, Las Vegas and nondeterminism for two-way finite automata. The three main results of this paper are the following ones. (i) If, for a regular language L, there exist small two-way nondeterministic finite automata for both L and LC, then there exists a small two-way Las Vegas finite automaton for L. (ii) There is a quadratic gap between nondeterminism and Las Vegas for two-way finite automata. (iii) For every k ∈ N, there is a regular language Sk such that Sk can be accepted by two-way Las Vegas finite automaton with O(k) states, but every two-way deterministic finite automaton recognizing Sk has at least Ω(k2= log2 k) states.
TL;DR: In this paper, the dynamical behavior of the Quantum Cellular Automaton (QCA) is described as a Markov Process, and emergent properties of the discrete dynamical QCA system are defined in the context of the characteristic polynomial of the Markov transition matrix.
Abstract: The dynamical behavior of the Quantum Cellular Automaton (QCA) is described here as a Markov Process. Ergodicity and recurrence, emergent properties of the discrete dynamical QCA system, are defined in the context of the characteristic polynomial of the Markov transition matrix. Except for a few anomalous cases, the transition matrix can be used to predict recurrence times. Finally, a correspondence between recurrence and elementary particle mass is proposed as an example of an emergent property of the QCA system. © 1999 Elsevier Science Ltd. All rights reserved.
TL;DR: Two discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule.
Abstract: A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in (1+1) dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called Model A in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called Model B, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, Model B shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.
TL;DR: This work would like to use heuristic programming to design new molecules and structures in the space of cellular automata, and is investigating mapping relations between a cellular automaton rule table and the chemical physics of real-world materials.
TL;DR: Families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time are determined.
Abstract: We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average probabilistic totalistic rule'' exhibiting the same periodic behavior.
TL;DR: A cluster-approximation mean-field scheme, which may be used to describe some cellular automaton (CA) models, is introduced based on analyzing the evolution of cluster states, based on a surface-reaction-like CA model very similar to the model of Ziff, Gulari, and Barshad.
Abstract: A cluster-approximation mean-field scheme, which may be used to describe some cellular automaton (CA) models, is introduced based on analyzing the evolution of cluster states. In this scheme the description of microscopic processes is exact within a cluster, and approximate for the interaction between clusters and the environment. The approach to building the theory is illustrated by a surface-reaction-like CA model very similar to the model of Ziff, Gulari, and Barshad. A set of equations of motion concerning the evolution of microscopic cluster states is derived, and some results from these equations are given.
01 Jan 1999
TL;DR: The computational results showed that the cellular automaton model has an ability to generate various biomimetic topological structures and the potentiality is related with diversity of life.
Abstract: We proposed the cellular automaton model based on remodeling of living systems. The computational results showed that the model has an ability to generate various biomimetic topological structures. The initial distribution of Young’s modulus greatly affects the topological formation. The formation is uniquely determined once the mechanical conditions are given. However, it is difficult to predict the final topological structure. These features suggest to us that a distributed mechanical system has potentiality to generate various topological structures and the potentiality is related with diversity of life.
01 Jan 1999
TL;DR: This work translates a standard approach of Field Theory into the framework of Cellular Automata to construct a parametrised class of stochastic 2D CA models simulating general explosion phenomena, which exhibit morphological instabilities and phase transitions from bounded to unbounded growth.
Abstract: We translate a standard approach of Field Theory into the framework of Cellular Automata (CA) to construct a parametrised class of stochastic 2D CA models simulating general explosion phenomena. The models exhibit morphological instabilities and phase transitions from bounded to unbounded growth.
TL;DR: In this paper, a variable structure learning automaton network with periodic random environment is proposed, which can be used for tracking some periodic nonstationary environment for which an upper bound on the period is known.
Abstract: Learning automata select an action from a finite set of their available actions and update their strategy on the basis of response received from the random environment using what is known as a reinforcement scheme. As an environment changes, the ordering of the actions with performance criterion may vary. If a learning automaton with a fixed strategy is used in such an environment, it may become less expedient with time and even inexpedient. However, using the learning scheme that has sufficient flexibility to track the better actions makes the performance improved. In this paper, a variable structure learning automaton network with periodic random environment is proposed. The results of some numerical simulations show that our model can be used for tracking some periodic nonstationary environment for which an upper bound on the period is known. © 1999 Scripta Technica, Electr Eng Jpn, 129(1): 3945, 1999