Showing papers on "Continuous automaton published in 2014"
TL;DR: Based on previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.
Abstract: Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.
26 citations
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TL;DR: A novel framework of reservoir computing for additive cellular automaton rules, which provides a direct way for concept building and symbolic processing, and it is much more efficient compared to state-of-the-art approaches.
Abstract: We introduce a novel framework of reservoir computing 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 Also, for additive cellular automaton rules, reservoir features can be combined using Boolean operations, which provides a direct way for concept building and symbolic processing, and it is much more efficient compared to state-of-the-art approaches
23 citations
TL;DR: A numerical technical of discontinuous cellular automaton method for crack growth analysis without remeshing is developed in this paper, where the level set method is employed to track the crack location and its growth path.
14 citations
17 Oct 2014
TL;DR: This work shows that for any given deterministic MFA, one can construct a reversible MFA with the same number of heads that accepts the same language as the former, and applies this conversion method to a Turing machine.
Abstract: A two-way multi-head finite automaton (MFA) is a variant of a finite automaton consisting of a finite-state control, a finite number of heads that can move in two directions, and a read-only input tape. Here, we show that for any given deterministic MFA we can construct a reversible MFA with the same number of heads that accepts the same language as the former. We then apply this conversion method to a Turing machine. By this, we can obtain, in a simple way, an equivalent reversible Turing machine that is garbage-less, uses the same number of tape symbols, and uses the same amount of the storage tape.
14 citations
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TL;DR: It is proved that with high probability an automaton admits a synchronizing word of length smaller than n^(1+\epsilon), and therefore that the Cerny conjecture holds withhigh probability.
Abstract: A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then it has a synchronizing word of size at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization by proving that with high probability, an automaton has a synchronizing word. In this article, we prove that with high probability an automaton admits a synchronizing word of length smaller than n^(1+\epsilon), and therefore that the Cerny conjecture holds with high probability.
11 citations
02 Sep 2014
TL;DR: This paper gives a construction, which for any given timed automaton produces a timed bisimilar automaton with the least number of clocks, and shows that such an automaton can be constructed in time that is doubly exponential in the number of clock of the original automaton.
Abstract: Model checking timed automata becomes increasingly complex with the increase in the number of clocks. Hence it is desirable that one constructs an automaton with the minimum number of clocks possible. The problem of checking whether there exists a timed automaton with a smaller number of clocks such that the timed language accepted by the original automaton is preserved is known to be undecidable. In this paper, we give a construction, which for any given timed automaton produces a timed bisimilar automaton with the least number of clocks. Further, we show that such an automaton with the minimum possible number of clocks can be constructed in time that is doubly exponential in the number of clocks of the original automaton.
8 citations
TL;DR: In this article, the authors introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton, which does not require any global operations or complex decoding algorithms.
Abstract: We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed of small local memories, communicating with neighbours, and repeatedly performing identical simple update rules. This approach does not require any global operations or complex decoding algorithms. Our cellular automata draw inspiration from classical field theories, with a Coulomb-like potential naturally emerging from the local dynamics. For a 3D automaton coupled to a 2D toric code, we present evidence of an error correction threshold above 6.1% for uncorrelated noise. A 2D automaton equipped with a more complex update rule yields a threshold above 8.2%. Our framework provides decisive new tools in the quest for realising a passive dissipative quantum memory.
7 citations
10 Dec 2014
TL;DR: Two numerical results are given in which the particular orbit of the automaton has some fractal structures and it is shown that the boundaries of the spatio patterns are fractal curves as time approaches infinity.
Abstract: Ulam's cellular automaton, a nonlinear two-dimensional cellular automaton, was introduced by Stanislaw Ulam for emulating crystalline growths. In this paper we give two numerical results in which the particular orbit of the automaton has some fractal structures. First result is that the boundaries of the spatio patterns are fractal curves as time approaches infinity. Second, we study the number of cells consisting the spatio patterns for each time step. We show that the dynamics of the number can be represented by Lebesgue's singular function.
7 citations
TL;DR: In this article, it is shown that Ulam's cellular automata contain a linear chaotic elementary cellular automaton (Rule 150) as a subsystem, and that the partial differential equation obtained by the inverse ultradiscretization preserves the self-organizing pattern of the Ulam automata.
Abstract: In this paper we study Ulam's cellular automaton, a nonlinear almost equicontinuous two-dimensional cell-model of crystalline growths. We prove that Ulam's automaton contains a linear chaotic elementary cellular automaton (Rule 150) as a subsystem. We also study the application of the inverse ultradiscretization, a method for deriving partial differential equations from a given cellular automaton, to Ulam's automaton. It is shown that the partial differential equation obtained by the inverse ultradiscretization preserves the self-organizing pattern of Ulam's automaton.
6 citations
10 Dec 2014
TL;DR: Although it is quite difficult to design a similar representation of signals and their propagations to the case of standard cellular automata model, this work shows some examples of them in gellular automata.
Abstract: Recently a new cellular automaton model, gellular automaton is introduced. Each cell is separated by gel materials as 'walls' and it contains a solution with some chemical materials. The reactions of such materials are defined as the local transition rules of the system. Some of them dissolve or construct these walls. The dissolution of a wall causes the mixture of the materials of two neighboring cells and it invokes the succeeding reactions. Although it is quite difficult to design a similar representation of signals and their propagations to the case of standard cellular automata model, we show some examples of them in gellular automata.
6 citations
05 Aug 2014
TL;DR: In this article, it was shown that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language for reset words of a particular automaton.
Abstract: A deterministic finite automaton Open image in new window is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton Open image in new window to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.
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TL;DR: A new tool is introduced, called the orbit automaton, that describes the action of an automaton group on the subtrees corresponding to the orbits of the orbits in the tree that is used to find elements of infinite order in certain automaton groups for which other methods failed to work.
Abstract: We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work.
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TL;DR: It is shown that an automaton is synchronizing with probability 1 O( 1 n0.5k ) and presented an algorithm with linear in n expected time, while the best known algorithm is quadratic on each instance.
Abstract: We consider the first problem that appears in any application of synchronizing automata, namely, the problem of deciding whether or not a givenn-statek-letter automaton is synchronizing. First we general- ize results from (4),(5) for the case of strongly connected partial automata. Specifically we show that an automaton is synchronizing with probability 1 O( 1 n0.5k ) and present an algorithm with linear in n expected time, while the best known algorithm is quadratic on each instance. This re- sults are interesting due to applications in synchronization of finite state information sources. Next we consider the synchronization of reachable partial automata that has application for splicing systems in the theory of computational biol- ogy. For this case we prove that the problem of testing a given automaton for synchronization is NP-complete.
TL;DR: In this article, the ultradiscrete solutions of the cellular automaton sine-Gordon equation were analyzed and linked to the discrete, lattice, sine−Gordon equation.
Abstract: We analyse the solutions of the cellular automaton sine–Gordon equation and link them to solutions of the discrete, lattice, sine–Gordon. We show that while the ultradiscretizable, positive definite, solutions of the latter behave dispersively, certain parts of these dispersive waves nonetheless survive in the ultradiscrete limit, giving rise to the solutions of the cellular automaton. We examine the ultradiscrete solutions in the case of a generalized cellular automaton in which the dependent variable can assume non-integer values and we show that the collision of two solitary waves is inelastic, leading to the creation of a 'bridge' of constant height that links two outgoing structures. Based on the ultradiscrete form of the sine–Gordon equation we explain the appearance of this bridging region and we describe its interaction with a solitary wave.
TL;DR: A refination method based on a cyclic cellular automaton (CCA) that simulates a crystallization-like process, aided with a heuristic evolutionary method called differential evolution (DE) used to perform an ordered search of full photonic band gaps in a 2D photonic crystal (PC).
Abstract: We present a refination method based on a cyclic cellular automaton (CCA) that simulates a crystallization-like process, aided with a heuristic evolutionary method called differential evolution (DE) used to perform an ordered search of full photonic band gaps (FPBGs) in a 2D photonic crystal (PC). The solution is proposed as a combinatorial optimization of the elements in a binary array. These elements represent the existence or absence of a dielectric material surrounded by air, thus representing a general geometry whose search space is defined by the number of elements in such array. A block-iterative frequency-domain method was used to compute the FPBGs on a PC, when present. DE has proved to be useful in combinatorial problems and we also present an implementation feature that takes advantage of the periodic nature of PCs to enhance the convergence of this algorithm. Finally, we used this methodology to find a PC structure with a 19% bandgap-to-midgap ratio without requiring previous information of suboptimal configurations and we made a statistical study of how it is affected by disorder in the borders of the structure compared with a previous work that uses a genetic algorithm.
TL;DR: In this paper, the authors introduce the discrete automaton models of gene networks with weight functions of vertices accounting for the various forms of the regulatory interaction of agents, and study the discrete mapping that describes the operation of a fragment of the gene network of the bacteria E. coli.
Abstract: We introduce the discrete automaton models of gene networks with weight functions of vertices accounting for the various forms of the regulatory interaction of agents. We study the discrete mapping that describes the operation of a fragment of the gene network of the bacteria E. coli. For this mapping, we find its fixed points (stationary states) on using the SAT approach. We also study the mappings that are defined by the random graphs of the network which we generate in accordance with the Gilbert-Erdos-Renyi and Watts-Strogatz models. For these mappings, we find the fixed points and the length 2 and 3 cycles. This article can be regarded as a survey of our results on the discrete models of gene networks and the numerical methods for studying their operation.
10 Dec 2014
TL;DR: It is shown that the Game of Life can be embedded into a simpler ACA with von Neumann neighborhood that takes 5 cell states and tens of transition rules.
Abstract: Emulating the global transitions of synchronous cellular automata (CAs), like the well-known Game of Life (GL), is a conventional scheme for computing on asynchronous cellular automata (ACAs). Especially, the GL can be completely simulated by an ACA with Moore neighborhood (Lee et al., 2004), which requires 8 states per cell and hundreds of transition rules. The simulation can be made much more efficient if we employ a continuous block of cells in an ACA to emulate each cell in the GL, by laying out a logic circuit on every block to accomplish the functionality of a GL's cell. Based on an efficient circuit scheme (Lee et al., 2014), we show that the GL can be embedded into a simpler ACA with von Neumann neighborhood that takes 5 cell states and tens of transition rules.
Journal Article•
TL;DR: In this article, the first known example of a physically universal cellular automata 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.
TL;DR: It is proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence proposed in the paper.
Abstract: Hybrid automaton is a formal model for precisely describing a hybrid
system in which the computational processes interact with the physical
ones. The reachability analysis of the polynomial hybrid automaton is
decidable, which makes the Taylor approximation of a hybrid automaton
applicable and valuable. In this paper, we studied the simulation relation
among the hybrid automaton and its Taylor approximation, as well as
the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid
automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper.
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TL;DR: A finite almost periodic augmented region automaton, which includes a clock measuring the global time and the timestamp of the automaton: the union of all its observable timed traces, which contains all the dates on which events occur - a generalization of the reachability problem.
Abstract: Given a non-deterministic timed automaton with silent transitions (eNTA), we show that after an initial stage it becomes time-periodic. After computing the periodic parameters, we construct a finite almost periodic augmented region automaton, which includes a clock measuring the global time. In the next step we construct the timestamp of the automaton: the union of all its observable timed traces, which contains all the dates on which events occur - a generalization of the reachability problem. The timestamp of each event is an almost periodic subset of the non-negative reals. We also construct a simple deterministic timed automaton with the same timestamp as the given timed automaton, in contrast to the fact that the timed automaton itself may be non-determinizable. One application is the decidability of the $1$-bounded language inclusion problem for eNTA. Another is a partial method, which is not bounded by time or number of steps, for showing the non-inclusion of languages of timed automata.
07 Jul 2014
TL;DR: A one-dimensional reversible cellular automaton is constructed that is computationally universal in a rather strong sense while being highly non-sensitive to initial conditions as a dynamical system.
Abstract: We construct a one-dimensional reversible cellular automaton that is computationally universal in a rather strong sense while being highly non-sensitive to initial conditions as a dynamical system. The cellular automaton has no sensitive subsystems. The construction is based on a simulation of a reversible Turing machine, where a bouncing signal activates the Turing machine to make single steps whenever the signal passes over the machine.
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TL;DR: In this paper, the authors studied the rule 150 elementary cellular automaton in terms of the distribution of the spacings of the singular values of the matieces obtained from proper time evolutions patterns.
Abstract: We studied the rule 150 elementary cellular automaton in terms of the distribution of the spacings of the singular values of the matieces obtained from proper time evolutions patterns. The distribution has strong resembrance to that of the random matrices which is derived from Painlev\'e V equation. Some analytic results for the relative period of the ECS are also presented.
12 Jul 2014
TL;DR: It is proposed that this 2D cellular automaton with rules that are a non-uniform generalization of a Moore-neighbourhood, outer-totalistic, two-state ("life-like") Cellular automaton has properties that make it useful as a model of an artificial chemistry with the potential for supporting open-ended evolutionary growth.
Abstract: We present a novel 2D cellular automaton with rules that are a non-uniform generalization of a Moore-neighbourhood, outer-totalistic, two-state ("life-like") cellular automaton. The system is purely deterministic and exhibits interesting multi-scale emergent behaviour, including the spontaneous formation of mobile particles and other self-organizing structures. In particular, smaller-scale structures can be shown to combine with other structures to form inhomogeneous higher-order constructions, and to do so at multiple orders of magnitude. The system has features in common with reaction-diffusion models. We propose that this system has properties that make it useful as a model of an artificial chemistry with the potential for supporting open-ended evolutionary growth. We call it Nu-life.
TL;DR: This paper proposes a homogeneous systolic automaton with n-dimensional layers (n-HSPA), and investigates some properties of real-time n-HSPas, and shows the recognizability of n- dimensional connected tapes by real- time n- HSPA’s.
Abstract: Cellular automata were investigated not only in the viewpoint of formal language theory, but also in the viewpoint of pattern recognition. Cellular automata can be classified into some types. A systolic pyramid automata is also one parallel model of various cellular automata. A homogeneous systolic pyramid automaton with n-dimensional layers (n-HSPA) is a pyramid stack of n-dimensional arrays of cells in which the bottom n-dimensional layer (level 0) has size an (a≥1), the next lowest (a-1)n, and so forth, the (a-1)st n-dimensional layer (level (a-1)) consisting of a single cell, called the root. Each cell means an identical finite-state machine. The input is accepted if and only if the root cell ever enters an accepting state. An n-HSPA is said to be a real-time n-HSPA if for every n-dimensional tape of size a n (a≥1) it accepts the n-dimensional tape in time a-1. Moreover, a 1- way n-dimensional cellular automaton (1-nCA) can be considered as a natural extension of the 1-way two- dimensional cellular automaton to n-dimension. The initial configuration is accepted if the last special cell reaches a final state. A 1-nCA is said to be a real- time 1-nCA if when started with n-dimensional array of cells in nonquiescent state, the special cell reaches a final state. In this paper, we propose a homogeneous systolic automaton with n-dimensional layers (n-HSPA), and investigate some properties of real-time n-HSPA. Specifically, we first investigate a relationship between the accepting powers of real-time n-HSPA’s and real-time 1-nCA’s. We next show the recognizability of n-dimensional connected tapes by real-time n-HSPA’s.
15 Nov 2014
TL;DR: This note will investigate periodicities of some hybrid cellularautomata con gured with rule 102 and 60 and null boundary condition.
Abstract: . We investigate periodicities of some hybrid cellular au-tomata con gured with rule 102 and 60 and null boundary condi-tion. 1. IntroductionCellular automata have been demonstrated by many researchers tobe a good computational model for physical systems simulation sincethe concept of cellular automata rst introduced by John Von Neumannin the 1950’s. And researchers have studied on cellular automata con- gured with rules 51, 60, 102, 153, 195 or 204 [1-7].In this note, we will investigate periodicities of some hybrid cellularautomata con gured with rule 102 and 60 and null boundary condition.2. PreliminariesA cellular automaton (CA) is an array of sites (cells) where eachsite is in any one of the permissible states. At each discrete time step(clock cycle) the evolution of a site value depends on some rule (thecombinational logic) which is a function of the present states of its kneighbors for a k-neighborhood CA. For a 2-state 3-neighborhood CA,the evolution of the (i)th cell can be represented as a function of thepresent states of (i 1)th, (i)th, and (i + 1)th cells as: x
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TL;DR: In this paper, a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function are formulated to satisfy heuristic criteria derived from elementary cellular automata.
Abstract: We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata. Behaviors characterized through these metrics are growth, decrease, chaoticity, and stability. From these metrics, two measures of global behavior are calculated: 1) a static measure that considers all possible input patterns and counts the occurrence of the proposed metrics in the truth table of the minimal Boolean form of the automaton; 2) a dynamic measure, corresponding to the mean of the behavioral metrics in $n$ executions of the automaton, starting from $n$ random initial states. We use these measures to characterize a cellular automaton and guide a genetic search algorithm, which selects cellular automata similar to the Game of Life. Using this method, we found an extensive set of complex binary cellular automata with interesting properties, including self-replication.
01 Jan 2014
TL;DR: The cellular automaton(CA)traffic flow model can be a good candidate for modeling the synchronized flow, since there is enough flexibility in the framework.
Abstract: In this paper,we further analyze our cellular automaton(CA)traffic flow model.By changing some parameters,the characteristics of our model can be significantly varied,ranging from the features of phase transitions to the number of traffic phases.We also review the other CA models based on Kerner’s three-phase traffic theory.By comparisons,we find that the core concepts for modeling the synchronized flow in these models are similar.Our model can be a good candidate for modeling the synchronized flow,since there is enough flexibility in our framework.
01 Mar 2014
TL;DR: In this paper, the ergodicity and power rule of a cellular automaton were investigated and the relation of topological pressure between the original automaton and its power rule was expressed in a closed form.
Abstract: This paper investigates the ergodicity and the power rule of the topological pressure of a cellular automaton. If a cellular automaton is either leftmost or rightmost premutive (due to the terminology given by Hedlund [Math.~Syst.~Theor.~3, 320-375, 1969]), then it is ergodic with respect to the uniform Bernoulli measure. More than that, the relation of topological pressure between the original cellular automaton and its power rule is expressed in a closed form. As an application, the topological pressure of a linear cellular automaton can be computed explicitly.
26 Sep 2014
TL;DR: It is shown that the endomorphism monoid E(A · B) of automaton A· B is a Clifford monoid, which generalizes and extends the representations of strongly connected automata and cyclic commutative automaton CCA.
Abstract: The Cartesian composition A ? B of a strongly connected automaton Group A and a cyclic commutative automaton Group B is defined. It is shown that the endomorphism monoid E(A ? B) of automaton A? B is a Clifford monoid. Finally, a representation of A ? B is provided by regular Clifford monoid matrix type automaton. This generalizes and extends the representations of strongly connected automata and cyclic commutative automaton CCA.