Showing papers on "Continuous automaton published in 1995"
04 Jun 1995
TL;DR: The automaton is capable, like Langton's automaton and with comparable complexity, of simple self-replication, but it also provides (at the cost, naturally, of increased complexity) the option of attaching to the Automaton an executable program which will be duplicated and executed in each of the copies of the automaton.
Abstract: We present a new self-reproducing cellular automaton capable of construction and computation beyond self-reproduction. Our automaton makes use of some of the concepts developed by Langton for his self-reproducing automaton, but provides the added advantage of being able to perform independent constructional and computational tasks alongside self-reproduction. Our automaton is capable, like Langton's automaton and with comparable complexity, of simple self-replication, but it also provides (at the cost, naturally, of increased complexity) the option of attaching to the automaton an executable program which will be duplicated and executed in each of the copies of the automaton. After describing in some detail the self-reproduction mechanism of our automaton, we provide a non-trivial example of its constructional capabilities.
99 citations
TL;DR: The problem of deciding whether a configuration has a predecessor is shown to be NLOG-complete for one-dimensional cellular automata, and the question whether a target configuration occurs in the orbit of a source configuration may be P- complete, NP-complete or PSPACE-complete, depending on the type of cellular automaton.
71 citations
TL;DR: The author introduces the basics of cellular automata and presents ChaOs, the cellular automaton used in Chaosynth, the new sound synthesis system being developed by the author and others working at Edinburgh University.
Abstract: Chaosynth is a new sound synthesis system being developed by the author and others working at Edinburgh University. Chaosynth functions by generating a large amount of short sonic events, or particles, in order to form larger, complex sound events. This synthesis technique is inspired by granular synthesis. Most granular synthesis techniques, however, use stochastic methods to control the formation of sound events, while Chaosynth uses a cellular automaton. Following an introduction to the basics of granular synthesis, the author explains how Chaosynth’s technique works. He then introduces the basics of cellular automata and presents ChaOs, the cellular automaton used in Chaosynth. The article concludes with some final remarks and suggestions for further work.
68 citations
TL;DR: This paper deals with the question whether myxobacteria can aggregate due to slime trail following and a stochastic cellular automaton model from which a system of partial differential equations can be derived, a so-called chemotaxis-system.
Abstract: This paper deals with the question whether myxobacteria can aggregate due to slime trail following. The starting point is a stochastic cellular automaton model where the bacteria are particles moving due to the rules of a jump process. A simplified case of this automaton shows that the slime has to be produced in an extremely high amount to account for aggregation. This simplified cellular automaton is connected to a stochastic many particle system from which a system of partial differential equations can be derived, a so-called chemotaxis-system. Here a moderate interaction between the particles has to be taken into account. In the last part this system is analyzed numerically to see whether it reflects the results of the simplified cellular automaton.
51 citations
03 Apr 1995
TL;DR: A simple, reversible and universal partitioning automaton is described and it is shown that there are reversible PA and CA that are able to simulate any reversible PA or CA on any configuration.
Abstract: Partitioning automata (PA) are defined. They are equivalent to cellular automata (CA). Reversible sub-classes are also equivalent. A simple, reversible and universal partitioning automaton is described. Finally, it is shown that there are reversible PA and CA that are able to simulate any reversible PA or CA on any configuration.
33 citations
TL;DR: An algebraic model for hybrid systems is proposed and its usefulness is illustrated by proving theorems in realization theory using this viewpoint.
30 citations
TL;DR: Evidence is given that the condition a = c is a threshold of chaotic behavior: with probability asymptotic to 1, almost all of the gates are still stable and weak, but the state cycle size is unbounded.
Abstract: A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let a (respectively c) be the probability that the gate is assigned a constant function (respectively a noncanalyzing function, i.e., EQUIVALENCE or EXCLUSIVE OR). Previous work has shown that when a>c, with probability asymptotic to 1, the random automaton exhibits very stable behavior: Almost all of the gates stabilize, almost all of them are weak, i.e., they can be perturbed without affecting the state cycle that is entered, and the state cycle is bounded in size. This article gives evidence that the condition a = c is a threshold of chaotic behavior: with probability asymptotic to 1, almost all of the gates are still stable and weak, but the state cycle size is unbounded. In fact, the average state cycle size is superpolynomial in the number of gates. © 1995 Wiley Periodicals, Inc.
24 citations
03 Apr 1995
TL;DR: It is shown that cellular automata on any planar, modular graph are equivalent to cellular automaton on the grid Z2, and interpreted in terms of planar parallel machines.
Abstract: We study cellular automata on Cayley graphs from a computational point of view. We are interested in the following problem: given two Cayley graphs, can every cellular automaton on the first graph be simulated by a cellular automaton on the second one, and conversely? We give a sufficient condition for such a two-way simulation to exist. In particular, we show that cellular automata on any planar, modular graph are equivalent to cellular automata on the grid Z2. We interpret this result in terms of planar parallel machines.
21 citations
TL;DR: This article shows how to simulate any Turing Machine by an invertible cellular automaton with no loss of time and gives, as a corollary, an easier proof of this result.
Abstract: The issue of testing invertibility of cellular automata has been often discussed. Constructing invertible automata is very useful for simulating invertible dynamical systems, based on local rules. The computation universality of cellular automata has long been positively resolved, and by showing that any cellular automaton could be simulated by an invertible one having a superior dimension, Toffoli proved that invertible cellular automaton of dimension d≥2 were computation-universal. Morita proved that any invertible Turing Machine could be simulated by a one-dimensional invertible cellular automaton, which proved computation-universality of invertible cellular automata. This article shows how to simulate any Turing Machine by an invertible cellular automaton with no loss of time and gives, as a corollary, an easier proof of this result.
20 citations
TL;DR: In this model, particle motions are simulated in a cellular space with a Margolus neighborhood, which has good conservation properties and collision detectability and shows several applications in two-dimensional cellular space.
Abstract: A natural object such as a flame with smoke is featured in terms of ambiguous boundaries and complex motion. One way of modeling natural objects is by particle systems, which need a large amount of computation time to calculate interactions among the particles. This paper deseribes another way of modeling particle motions based on a cellular automaton. Cellular automata are massively parallel computation models that can simulate complex phenomena. In our model, particle motions are simulated in a cellular space with a Margolus neighborhood, which has good conservation properties and collision detectability. This paper shows several applications in two-dimensional cellular space.
18 citations
Posted Content•
TL;DR: If the blocked rule satisfies an identity which holds for a broad class of algebras, then the underlying rule must have essentially the same structure, and must depend only on its leftmost and rightmost inputs; roughly speaking, that the block transformation cannot turn a nonlinear rule into a linear one.
Abstract: By grouping several sites together into one, a cellular automaton can be transformed into another with more states and a smaller neighborhood; if the neighborhood has just two sites, we can think of the resulting CA rule as a binary operation. We show that if the blocked rule satisfies an identity which holds for a broad class of algebras, then the underlying rule must have essentially the same structure, and must depend only on its leftmost and rightmost inputs; roughly speaking, that the block transformation cannot turn a nonlinear rule into a linear one.
05 Jul 1995
TL;DR: This algorithm is based on the notion of failure function and mainly consists in efficiently constructing a new deterministic automaton, which is shown to be more efficient both in time and space than naive algorithms such as the powerset algorithm used for determinization.
Abstract: We present an algorithm permitting to search in a text for the patterns of a regular set. Unlike many classical algorithms, we shall assume that the input of the algorithm is a deterministic automaton and not a regular expression. Our algorithm is based on the notion of failure function and mainly consists in efficiently constructing a new deterministic automaton. This construction is shown to be more efficient both in time and space than naive algorithms such as the powerset algorithm used for determinization. In particular, its space complexity is linear in the size of the obtained automaton.
03 Apr 1995
TL;DR: It is proved that expansive CA are topologically mixing, and their topological entropies are logarithms of integers, if, in addition, the endow these CA with the uniform Bernoulli measure, it is the unique measure of maximal entropy for F.
Abstract: A one-sided one-dimensional cellular automaton F with radius r has associated a canonical factor defined by considering only the first r coordinates of all the images of points under the powers of F. Whenever the cellular automaton is surjective, this language defines a subshift which plays a primary role in its dynamics. In this article we study the class of expansive cellular automata, i.e. those that are conjugate to their canonical factor; they are surjective, and their canonical factor is always of finite type. This class is a natural generalization of the toggle or permutative cellular automata introduced in [H]. We prove that expansive CA are topologically mixing, and their topological entropies are logarithms of integers. If, in addition, we endow these CA with the uniform Bernoulli measure, we prove that it is the unique measure of maximal entropy for F. We also describe a family of non permutative expansive cellular automata.
TL;DR: The non-conservative noisy critical height sandpile cellular automaton with open boundary conditions is studied analytically on the Bethe lattice and the single-site probabilities, pair probabilities and avalanche size distributions for the three versions of the automaton are calculated.
Abstract: The non-conservative noisy critical height sandpile cellular automaton with open boundary conditions is studied analytically on the Bethe lattice. Using the modified method of Dhar and Majumdar (1990), the single-site probabilities, pair probabilities and the avalanche size distributions for the three versions of the automaton, with different amount of dissipated particles, are calculated.
TL;DR: It is shown how cellular automata may be used to model the behaviour of sequential circuits, and a discussion, supported by experimental data, on the criteria to be used for the choice of these functions.
Abstract: Cellular automata are powerful computational models for the study of physical systems. In the recent past they have been used to solve VLSI and CAD problems such as synthesis and testing of integrated circuits. In this paper it is shown how cellular automata may be used to model the behaviour of sequential circuits. The nice property of the proposed approach is that it provides an homogeneous representation of all the components of the circuit under investigation : primary inputs, flip-flops, primary outputs and their related cones of combinational logic are modelled in the same way by means of cellular automaton cells. Clearly, it is necessary to differentiate cells representing the flip-flops, from cells modelling the primary outputs and the primary inputs ; in fact, for cells of the first type the evolution rules are fixed, and they are simply given by the boolean functions realized by the cones of logic feeding the flip-flops. A similar argument applies to cells of the second type, with the difference that the states of these cells do not influence the next state of any other cell of the automaton. For cells of the third type, on the other hand, the next state functions are boolean functions whose characteristics depend on the aspect of the external world the user would like to model. The choice of such functions is not trivial, and to be effective requires an accurate study of both the functional meaning of each primary input in the context of the circuit to be modelled, and the relationship, if any, between the primary input lines. This paper includes a discussion, supported by experimental data, on the criteria to be used for the choice of these functions.