scispace - formally typeset
Search or ask a question

Showing papers on "Continuous automaton published in 2015"


Journal ArticleDOI
TL;DR: This work applies the new arithmetic to a cellular automaton forest-fire model which is connected with the percolation methodology and in some sense combines the dynamic and the static percolations problems and under certain conditions exhibits critical fluctuations.

46 citations


Book ChapterDOI
12 Oct 2015
TL;DR: Angluin’s \(L^*\) algorithm is harnessed for learning a deterministic finite automaton that describes the possible scenarios under which a given program error occurs and an abstract visual representation of errors and of program segments is presented.
Abstract: We propose to harness Angluin’s \(L^*\) algorithm for learning a deterministic finite automaton that describes the possible scenarios under which a given program error occurs. The alphabet of this automaton is given by the user (for instance, a subset of the function call sites or branches), and hence the automaton describes a user-defined abstraction of those scenarios. More generally, the same technique can be used for visualising the behavior of a program or parts thereof. This can be used, for example, for visually comparing different versions of a program, by presenting an automaton for the behavior in the symmetric difference between them, or for assisting in merging several development branches. We present initial experiments that demonstrate the power of an abstract visual representation of errors and of program segments.

38 citations


Journal ArticleDOI
TL;DR: This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation, and suggests that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing.
Abstract: This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells, and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking, What is the automobile of air?

38 citations


Posted Content
TL;DR: A novel framework of reservoir computing is introduced, that is capable of both connectionist machine intelligence and symbolic computation, and it is proved that cellular automaton reservoir holds a distributed representation of attribute statistics, which provides a more effective computation than local representation.
Abstract: We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is capable of long short-term memory and it requires orders of magnitude less computation compared to Echo State Networks. We prove that cellular automaton reservoir holds a distributed representation of attribute statistics, which provides a more effective computation than local representation. It is possible to estimate the kernel for linear cellular automata via metric learning, that enables a much more efficient distance computation in support vector machine framework. Also, binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing.

14 citations


Proceedings ArticleDOI
11 Jan 2015
TL;DR: The first known example of a physically universal CA is given, answering an open problem of Janzing and opening the way for further research in this area.
Abstract: Several cellular automata (CA) are known to be universal in the sense that one can simulate arbitrary computations (e.g., circuits or Turing machines) by carefully encoding the computational device and its input into the cells of the CA. In this paper, we consider a different kind of universality proposed by Janzing. A cellular automaton is physically universal if it is possible to implement any transformation on a finite region of the CA by initializing the complement of the region and letting the system evolve. We give the first known example of a physically universal CA, answering an open problem of Janzing and opening the way for further research in this area.

13 citations


Journal ArticleDOI
TL;DR: A cellular automaton analog of the multidimensional Allen–Cahn equation which is not an integrable system is constructed by the ultradiscretization, and the traveling wave solutions for the resulting Cellular automaton are given.
Abstract: Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. The cellular automaton constructed by this procedure preserves the essential properties of the original equation, such as the structure of exact solutions for integrable equations. In this article, a cellular automaton analog of the multidimensional Allen–Cahn equation which is not an integrable system is constructed by the ultradiscretization. Moreover, the traveling wave solutions for the resulting cellular automaton are given. The shape, behavior and stability of the solutions in ultradiscrete systems are similar to those in continuous systems.

11 citations


Journal ArticleDOI
TL;DR: A way to achieve a quasi- periodic like behaviour of RDA is presented and applicability of the model is extended to quasi-periodic phenomena, based on the same microscopic rule which produces exponential and inverse-power like distributions.
Abstract: Finite version of Random Domino Automaton — a recently proposed toy model of earthquakes — is investigated in detail. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for a system of large size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N ≥ 5 and propose appropriate approximations, the quality of which is studied in examples obtained within the framework of Markov chains.

8 citations


Proceedings Article
11 Dec 2015
TL;DR: A framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation that corresponds to a binary valued and nonlinear neuro-symbolic architecture is introduced.
Abstract: In this paper, we introduce a framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation Cellular automaton is used as the reservoir of dynamical systems A cellular automaton is a very sparsely connected network with logical nodes and nonlinear/logical connection functions, hence the proposed system corresponds to a binary valued and nonlinear neuro-symbolic architecture Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir In addition to being used as the feature representation for pattern recognition, binary reservoir vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way symbolic processing To demonstrate the capability of the proposed system, we make analogies directly on image data by asking 'What is the Automobile of Air'?, and make logical inference using rules by asking 'Which object is the largest?'

8 citations


Posted Content
TL;DR: A new Life-like cellular automaton capable of logic universality -- the X-rule, which is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is non-isotropic.
Abstract: We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is non-isotropic. We outline the search method. Several glider types and stable structures emerge spontaneously within X-rule dynamics. We construct glider-guns based on periodic oscillations between stable barriers, and interactions to create logical gates.

7 citations


Book ChapterDOI
08 Jun 2015
TL;DR: A quantum version of Janzing’s “physical universality”, a notion of computational universality for cellular automata which requires computations to be done directly on the cells, is explored.
Abstract: We explore a quantum version of Janzing’s “physical universality”, a notion of computational universality for cellular automata which requires computations to be done directly on the cells. We discuss physical universality in general, the issues specific to the quantum setting, and give an example of a quantum cellular automaton achieving a quantum definition of physical universality.

6 citations


Journal ArticleDOI
TL;DR: Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton with unconstrained topology and with the power to create new cells.
Abstract: Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.

Posted Content
TL;DR: This paper describes a proposal for an extended cellular automaton that is suited for support of quantum field theory and indicates that the classical CA may not be a sufficient basis for the modeling of more advanced physics theories, such as quantum field theories.
Abstract: Models of areas of physics in terms of cellular automata have become increasingly popular Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the dynamic evolution of such systems Because many areas of physics can be described by starting with a specific Lagrangian, the idea to derive a cellular automaton directly from the Lagrangian (or similar construct, such as the Hamiltonian or action) is not new Previous work, however, indicated that the classical CA may not be a sufficient basis for the modeling of more advanced physics theories, such as quantum field theory Specifically, the modeling of interactions in quantum field theory requires extensions and modifications of the classical CA This paper describes a proposal for an extended cellular automaton that is suited for support of quantum field theory

Posted Content
TL;DR: It is proved that there is a weakly universal cellular automaton on the pentagrid with two states and a previous result with three states is rotation invariant while the result of the present paper is not.
Abstract: In this paper, we construct a cellular automaton on the pentagrid which is planar, weakly universal and which have five states only. This result much improves the best result which was with nine states

Journal ArticleDOI
TL;DR: This work applies the new arithmetic to a cellular automaton forest-fire model which is connected with the percolation methodology and in some sense combines the dynamic and the static percolations problems and under certain conditions exhibits critical fluctuations.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the inactive-active phase transition in an array of additive cellular automata under noise and show that their phase transition belongs to the directed percolation universality class of critical behavior.
Abstract: We investigate the inactive-active phase transition in an array of additive (exclusive-or) cellular automata under noise. The model is closely related with the Domany-Kinzel probabilistic cellular automaton, for which there are rigorous as well as numerical estimates on the transition probabilities. Here we characterize the critical behavior of the noisy additive cellular automaton by mean field analysis and finite-size scaling and show that its phase transition belongs to the directed percolation universality class of critical behavior. As a by-product of our analysis, we argue that the critical behavior of the noisy elementary CA 90 and 102 (in Wolfram's enumeration scheme) must be the same. We also perform an empirical investigation of the mean field equations to assess their quality and find that away from the critical point (but not necessarily very far away) the mean field approximations provide a reasonably good description of the dynamics of the PCA.

Journal ArticleDOI
TL;DR: This work interprets the topological concepts of cellular automata as graphs and vector spaces in order to provide a suitable mathematical framework for analysis and leads to evolution systems (strongly continuous semigroups, abstract Cauchy problems) on the one hand and stochastic processes on the other.

Posted Content
TL;DR: In this article, the authors present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata, i.e. images that show the average state of each cell during the evolution of the automata.
Abstract: In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.

Journal ArticleDOI
TL;DR: This paper presents the first algorithm for LZ trie construction that runs in effectively linear time thereby making it an attractive choice for finite‐state automata implementation and presents two variants of the construction procedure – an optimal method regarding the final size and a method that sacrifices some compression for low intermediate memory usage.
Abstract: Finite-state automata are important components in information retrieval and natural language processing software. A recursive automaton is the most compact representation of the acyclic deterministic finite-state automata. It is based on merging not only the equivalent states but also the identical substructures in an automaton. The LZ trie variant is the state-of-the-art in automata compression regarding space, but the time needed for its construction was, until now, quadratic, which has made it impractical for large inputs. In this paper, we present the first algorithm for LZ trie construction that runs in effectively linear time thereby making it an attractive choice for finite-state automata implementation. We achieve this goal by adding a new functionality to the enhanced suffix array data structure. We present two variants of the construction procedure - an optimal method regarding the final size and a method that sacrifices some compression for low intermediate memory usage. We have made the implementation of our algorithms available in an open source software package LzLex.Copyright © 2014 John Wiley & Sons, Ltd.

Proceedings ArticleDOI
01 Jan 2015
TL;DR: It is proved a characterisation of \mu-limit sets of two-dimensional cellular automata, extending existing results in the one-dimensional case, that describe the typical asymptotic behaviour of the cellular automaton.
Abstract: We prove a characterisation of \mu-limit sets of two-dimensional cellular automata, extending existing results in the one-dimensional case. This sets describe the typical asymptotic behaviour of the cellular automaton, getting rid of exceptional cases, when starting from the uniform measure.

19 May 2015
TL;DR: A general definition of automata with fuzzy states is provided which includes as its special cases automata used by Lin et al.
Abstract: In this paper we provide a general definition of automata with fuzzy stateswhich includes as its special cases automata used by Lin et al. [29], Liu and Qiu [30,31,42]and Xing et al. [56] in the study of fuzzy discrete event systems, as well as various typesof automata constructed in [14,15,18,32] for the purpose of the determinization of fuzzyautomata. We explain the relationships between these differentmodels of automata withfuzzy states and showthat every crisp-deterministic fuzzy automaton can be transformedinto a language-equivalent automaton with fuzzy states, and vice versa.

Proceedings ArticleDOI
01 Oct 2015
TL;DR: This paper presents a method for the implementation of a mirror object within the Game of Life cellular automaton, based on quantum states that eliminates self-interference, thereby enabling a continuous progression of translating patterns.
Abstract: This paper presents a method for the implementation of a mirror object within the Game of Life cellular automaton, based on quantum states. While in the nominal case, the application of a regular mirror causes any reflected pattern to degenerate, reflection based on quantum states eliminates self-interference, thereby enabling a continuous progression of translating patterns.

Posted ContentDOI
TL;DR: In this paper, a cellular automaton is called post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymmptotic to a preimage of the other.
Abstract: We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.

Journal ArticleDOI
TL;DR: This paper defines an analytic function of the local rules of an Elementary Cellular Automaton by constructing the recognition function ofthe states of the cell and the neighbors and shows that the programming structure is optimized and the programming efficiency is enhanced.


Proceedings ArticleDOI
26 Oct 2015
TL;DR: A novel optimal directed control problem where the selection of the controllable event at each state is determined so as to maximize the worst-case value of the mean payoffs of controlled behaviors subject to a given linear temporal logic control specification.
Abstract: We consider a quantitative discrete event system modeled by a weighted automaton, where a weight assigned to each transition represents a cost by the occurrence of the transition. An optimal directed controller selects at most one controllable event at each state to optimize director's cost of the controlled discrete event system. On the other hand, linear temporal logic is often used to specify the qualitatively desired behavior of a discrete event system. In this paper, we formulate a novel optimal directed control problem where the selection of the controllable event at each state is determined so as to maximize the worst-case value of the mean payoffs of controlled behaviors subject to a given linear temporal logic control specification. We propose a design method using a two-player game automaton whose players are the director and the product automaton. The former aims to maximize the worst-case value of the generated behaviors while the latter wants to minimize it. Under this situation, we use the concept of a best response and provide an algorithm to compute an optimal director. Then, we apply the proposed algorithm to a control problem of an AGV.

Journal ArticleDOI
TL;DR: The definition of a letter-to-letter transducer that computes the relation induced by a one-rule length-preserving string rewrite system and it is proved that this automaton is finite if and only if the corresponding relation is rational.
Abstract: In this work, we use rearrangements in rewriting positions sequence in order to study precisely the structure of the derivations in one-rule length-preserving string rewrite systems. That yields to the definition of a letter-to-letter transducer that computes the relation induced by a one-rule length-preserving string rewrite system. This transducer can be seen as an automaton over an alphabet A × A . We prove that this automaton is finite if and only if the corresponding relation is rational. We also identify a sufficient condition for the context-freeness of the language L recognized by this automaton and, when this condition is satisfied, we construct a pushdown automaton that recognizes L.

Journal ArticleDOI
TL;DR: It is concluded that the results that are obtained make it possible to construct an analogue of the statistics collection procedure for the field of fuzzy systems, based on a theory that generalizes Markov chains and the axiomatic description of operations with fuzzy evidence.
Abstract: The behavior of M.L. Tsetlin's automaton with linear tactics in a fuzzy environment is considered. The behavior of such an automaton was previously studied in a random environment, where the classical apparatus of probabilistic Markov chains could be used. This work is based on two results that were previously obtained by the author, namely, a theory that generalizes Markov chains and the axiomatic description of operations with fuzzy evidence. The explicit formulas for describing the behavior of the automaton that were obtained in this paper suggest a deep analogy with the results of M.L. Tsetlin. In particular, it is shown that this automaton in a fuzzy environment also has the property of asymptotic optimality. As an application, we discuss the possibility of using this property to measure membership functions for values that are similar to singletons or point functions. It is concluded that the results that are obtained in this paper make it possible to construct an analogue of the statistics collection procedure for the field of fuzzy systems.

Posted Content
TL;DR: A one-dimensional version of the physically universal cellular automaton, which has the ability to implement an arbitrary transformation of spatial patterns.
Abstract: Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal cellular automaton. We construct a one-dimensional version of the automaton.


Journal ArticleDOI
TL;DR: A sperner’s grid is thought of a finite state system, where in the model the automation graphs of the various states gives rise to different groomable light paths in network.
Abstract: A sperner’s grid is thought of a finite state system, where in the model gives rise to an optimal network through characterization of paths .the automation graphs of the various states gives rise to different groomable light paths in network.