Showing papers on "Continuous automaton published in 2008"

Robust safety of timed automata

Abstract: Timed automata are governed by an idealized semantics that assumes a perfectly precise behavior of the clocks. The traditional semantics is not robust because the slightest perturbation in the timing of actions may lead to completely different behaviors of the automaton. Following several recent works, we consider a relaxation of this semantics, in which guards on transitions are widened by Δ>0 and clocks can drift by ?>0. The relaxed semantics encompasses the imprecisions that are inevitably present in an implementation of a timed automaton, due to the finite precision of digital clocks. We solve the safety verification problem for this robust semantics: given a timed automaton and a set of bad states, our algorithm decides if there exist positive values for the parameters Δ and ? such that the timed automaton never enters the bad states under the relaxed semantics.

The universal automaton.

Abstract: This paper is a survey on the universal automaton, which is an automaton canonically associated with every language. In the last forty years, many objects have been defined or studied, that are indeed closely related to the universal automaton. We first show that every automaton that accepts a given language has a morphic image which is a subautomaton of the universal automaton of this language. This property justifies the name “universal” that we have coined for this automaton. The universal automaton of a regular language is finite and can be effectively computed in the syntactic monoid or, more efficiently, from the minimal automaton of the language. We describe the construction that leads to tight bounds on the size of the universal automaton. Another outcome of the effective construction of the universal automaton is the computation of a minimal NFA accepting a given language, or approximations of such a minimal NFA. From another point of view, the universal automaton of a language is based on the factorisations of this language, and is thus involved in the problems of factorisations and approximations of languages. Last, but not least, we show how the universal automaton gives an elegant solution to the star height problem for some classes of languages (pure-group or reversible languages). With every language is canonically associated an automaton, called the universal automaton of the language, which is finite whenever the language is regular. It is large, it is complex, it is complicated to compute, but it contains, hopefully, many interesting informations on the language. In the last forty years, it has been described a number of times, more or less explicitly,

The theory of trackability with applications to sensor networks

Abstract: In this article, we formalize the concept of tracking in a sensor network and develop a quantitative theory of trackability of weak models that investigates the rate of growth of the number of consistent tracks given a temporal sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a nondeterministic finite automaton (a weak model) and the sensor network is modelled by an observer capable of detecting events related, typically ambiguously, to the states of the underlying automaton. Formally, an input string of symbols (the sensor network observations) that is presented to a nondeterministic finite automaton, M, (the weak model) determines a set of state sequences (the tracks or hypotheses) that are capable of generating the input string. We study the growth of the size of this candidate set of tracks as a function of the length of the input string. One key result is that for a given automaton and sensor coverage, the worst-case rate of growth is either polynomial or exponential in the number of observations, indicating a kind of phase transition in tracking accuracy. These results have applications to various tracking problems of recent interest involving tracking phenomena using noisy observations of hidden states such as: sensor networks, computer network security, autonomic computing and dynamic social network analysis.

Data mining with cellular automata

Abstract: A cellular automaton is a discrete, dynamical system composed of very simple, uniformly interconnected cells. Cellular automata may be seen as an extreme form of simple, localized, distributed machines. Many researchers are familiar with cellular automata through Conway's Game of Life. Researchers have long been interested in the theoretical aspects of cellular automata. This article explores the use of cellular automata for data mining, specifically for classification tasks. We demonstrate that reasonable generalization behavior can be achieved as an emergent property of these simple automata.

Polynomial-time verification of the observer property in abstractions

Abstract: This paper presents an algorithm to test if an abstraction obtained through natural projection has the observer property, without having to compute the abstraction. The original automaton and the set of events to be kept by the projection are inputs to the algorithm. An automaton, the verifier, is built such that the verification of the property becomes a verification of reachability of a special state. The complexity of the algorithm is polynomial in the size of the state space of the automaton. Two examples are presented to illustrate the algorithm.

Embedding finite automata within regular expressions

Abstract: Regular expressions and their extensions have become a major component of industry-oriented specification languages such as IEEE PSL [IEEE Standard for Property Specification Language (PSL). IEEE Std 1850(TM)-2005]. The model checking procedure of regular expression based formulas, involves constructing an automaton which runs in parallel with the model. In this paper we re-examine the automata construction. We propose an algorithm that allows an intermediate representation mixing both regular expressions and automata. This representation can be thought of as plugging an automaton inside a regular expression, to replace an existing sub-expression. In order to be verified, the intermediate representation is then translated into another automaton, resulting in a set of automata running in parallel. A key feature of this algorithm is that the plug-in automaton is independent of the regular expression from which it originated, and thus can be used in several different properties. We demonstrate the usefulness of our method by providing a set of applications. We show how the use of our method allows modularity and flexibility of the automata construction, and can increase expressiveness when seres are mixed with ctl. We give two applications for which it significantly reduces the size of the automata built for formulas, thus reducing the overall run time of the model checking procedure.

Multidimensional cellular automata and generalization of Fekete's lemma

Abstract: Fekete's lemma is a well-known combinatorial result on number sequences: we extend it to functions defined on d-tuples of integers. As an application of the new variant, we show that nonsurjective d-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.

Gate-Level Evolutionary Development Using Cellular Automata

Abstract: In this paper we present a novel evolutionary developmental technique for the design of the combinational circuits. This technique is based on the development one dimensional uniform cellular automaton. The goal is to evolve a cellular automaton - its local transition function and two different initial states from which a combinational circuit with a given functionality at the gate-level may be developed. The two evolved initial states are intended to demonstrate the ability of the developmental process to construct the given circuit by means of a single local transition function. Moreover, it will be shown that the developmental process is able to adapt also to other initial states than that were originally evolved, i.e. a working circuit possessing a different structure is created. The circuit functionality may be preserved even if the development of the cellular automaton continues after the original circuit was developed.

Radial View of Continuous Cellular Automata

Abstract: Continuous cellular automata (or coupled map lattices) are cellular automata where the state of the cells are real values in [0, 1] and the local transition rule is a real function. The classical observation medium for cellular automata, whether Boolean or continuous, is the space-time diagram, where successive rows correspond to successive configurations in time. In this paper we introduce a different way to visualize the evolution of continuous cellular automata called Radial Representation and we employ it to observe a particular class of continuous cellular automata called fuzzy cellular automata (FCA), where the local rule is the "fuzzification" of the disjunctive normal form that describes the local rule of the corresponding Boolean cellular automata. Our new visualization method reveals interesting dynamics that are not easily observable with the space-time diagram. In particular, it allows us to detect the quick emergence of spatial correlations among cells and to observe that all circular FCA from random initial configurations appear to converge towards an asymptotic periodic behavior. We propose an empirical classification of FCA based on the length of the observed periodic behavior: interestingly, all the minimum periods that we observe are of lengths one, two, four, or n (where n is the size of a configuration).

Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

Abstract: The rule 150 cellular automaton is a remarkable discrete dynamical system, as it shows 1∕fα spectra if started from a single seed [J Nagler and J C Claussen, Phys Rev E 71, 067103 (2005)] Despite its simplicity, a feasible solution for its time behavior is not obvious Its self-similarity does not follow a one-step iteration like other elementary cellular automata Here it is shown how its time behavior can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length This allows us to compute the total activity time series more efficiently than by simulating the whole spatiotemporal process or even by using the closed expression The results are further extended to the generalization of rule 150 to the two-dimensional case and to Bethe lattices and the relation to corresponding integer sequences is discussed

On the Analysis of Simple 2D Stochastic Cellular Automata

Abstract: We analyze the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight neighbors per cell) under fully asynchronous dynamics (where only one random cell updates at each time step). Even if 2D Minority seems a simple rule, from the experience of Ising models and Hopfield nets, it is known that models with negative feedback are hard to study. This automaton actually presents a rich variety of behaviors, even more complex than what was observed and analyzed in a previous work on 2D Minority for the von Neumann neighborhood (four neighbors per cell) [1], including particles and a wider range of stable configurations. Nevertheless our work suggests that predicting the behavior of this automaton although difficult is possible, opening the way to analyze the class of totalistic automata.

A particle displacement representation for conservation laws in two-dimensional cellular automata.

Abstract: The problem of describing the dynamics of a conserved energy in a cellular automaton in terms of local movements of “particles” (quanta of that energy) has attracted some people’s attention. The one-dimensional case was already solved by Fukś (2000) and Pivato (2002). For the two-dimensional cellular automata, we show that every (contextfree) conservation law can be expressed in terms of such particle displacements. Introduction Let L = Zd be the d-dimensional square lattice, and S a finite set of states. Every cellular automaton (CA for short) F : SL → SL maps the uniform configurations into the uniform configurations. Two configurations x, y : L→ S are asymptotic if they agree on all but finitely many cells of the lattice. The image of asymptotic configurations under every cellular automaton remain asymptotic. A (context-free) energy assignment is a function μ : S → R. The μ-content of a finite pattern p : A→ S (A ⊆ L finite) is the sumM(p) , ∑ i∈A μ (p[i]). For every two asymptotic configurations x, y ∈ SL, the corresponding energy difference is δM(x, y) , ∑ i∈L [μ(y[i])− μ(x[i])] (0.1) which is clearly well-defined (only a finite number of terms are non-zero). The energy μ is conserved by a cellular automaton F : SL → SL, if δM(Fx, Fy) = δM(x, y) (0.2)

Automaton model with variable cell size for the simulation of pedestrian flow

Abstract: The simulation of pedestrian flow is an important issue in many modern traffic systems and en- vironments. The planning and control of pedestrian flow is crucial for large buildings, shopping malls, airports, railway stations, cruise ships and ferries, manifestation places, sport stadiums etc., in order that optimal traffic throughput for daily usage can already be guaranteed at the time of construction. Even evacuation scenarios can be considered in this context. Common simulation approaches are either discrete or continuous. While continuous models, which rely on mathematical models originally developed for fluids and gases, are better suited for the modelling of somehow global phenomena, individual aspects are given more consideration in the discrete models. Many discrete models for pedestrian flow are based on cellular automata, however, traditional cellular automaton models work with a fixed cell size. Since at any given time, the states of the cells are always well-defined by the automaton's transition rules, the current simulation object positioned in a grid cell can be considered as the cell state accordingly. In view of the original definition of the cellular automaton, we can understand the cell size as the minimal two-dimensional space the simulation objects (e.g. pedestrians) reserve for themselves exclusively. In the current paper, we present a two-dimensional automaton model to simulate pedestrian flow in which the cell size can be dynamically modified in a virtual manner. It can be easily observed in real world scenarios that the aforesaid minimal but exclusive space a pedestrian takes may be "elastic" (variable), especially when pedestrian density and the discrepancy of the flow-in and flow-out rates of the system are given sufficient consideration. Thus, this virtual flexibility of the cell size is favourable and necessary in the simulation of pedestrian flow where the minimal space required by a pedestrian is not confined to be constant. The virtual cell size in our model is constructed to be dependent on the actual pedestrian density. In the concluding section, we discuss the possibility of extending this model for the application of anisotropic neighbourhoods. The present work represents a continuation and extension of (1) and (3). By introducing the concept of variable cell size and two different implementations for it, we significantly extend the applicability of cellular automaton models for the discrete simulation of pedestrian flow.

Advancing density waves and phase transitions in a velocity dependent randomization traffic cellular automaton

Abstract: Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions between these phases, allows us to establish a rigorous classification based on their tempo-spatial behavioral characteristics. As a result from the system's complex dynamics, its flow-density relation exhibits a non-concave region in which forward propagating density waves are encountered. All four phases furthermore share the common property that moving vehicles can never increase their speed once the system has settled into an equilibrium.

Necessary Conditions for the Optimality of the Automaton Part of a Logical-Dynamical System

Abstract: A dynamical system controlled by an automaton with memory is considered. The continuous part of the system is described by differential equations, and the automaton part, by recurrence inclusions. The instants of time at which the state of the automaton part is changed are not known in advance and are determined during the optimization process. Moreover, modes with multiple switchings of the automaton part at a given instant of time are admitted. Necessary conditions for the optimality of a program control are obtained. The application of the optimality conditions is illustrated by examples.

Quantization of cellular automata

Abstract: Technische Universit¨at BraunschweigIMaPh, Mendelssohnstrase 338106 Braunschweig DEUTSCHLANDE-mail address: vincent.nesme@tu-bs.deAbstract. Take a cellular automaton, consider that each configuration is a basis vectorin some vector space, and linearize the global evolution function. If lucky, the result couldactually make sense physically, as a valid quantum evolution; but does it make sense asa quantum cellular automaton? That is the main question we address in this paper. Inevery model with discrete time and space, two things are required in order to qualify asa cellular automaton: invariance by translation and locality. We prove that this localitycondition is so restrictive in the quantum case that every quantum cellular automatonconstructed in this way — i.e., by linearization of a classical one — must be reversible. Wealso discuss some subtleties about the extent of nonlocality that can be encountered in theone-dimensional case; we show that, even when the quantized version is non local, still,under some conditions, we may be unable to use this nonlocality to transmit informationnonlocally.

Different Types of Linear Fuzzy Cellular Automata and their Applications

Abstract: A linear array of interconnected fuzzy automaton is called linear fuzzy cellular automaton. It is shown that the language class of linear fuzzy cellular automata strictly contains the language class of linear cellular automata. This justifies the wide spread use of linear fuzzy cellular automaton as is evident from the literature. In this paper a special type of cellular automaton (CA) model is investigated. This CA model computes effect due to interaction of neighboring cells and effect due to external disturbance on the cells simultaneously. The transition due to both the effects may be represented by a single function which is the composition of two functions. Further it is shown that the class of language accepted by linear hybrid fuzzy cellular automata is included in the class of language accepted by linear hybrid fuzzy cellular automata with external input(HFCAI). HFCAI is useful for computing growth in evolutionary systems which are also affected by external cause.

Marker versus inkdot over three-dimensional patterns

Abstract: A multi-marker automaton is a finite automaton which keeps marks as pebbles in the finite control, and cannot rewrite any input symbols but can make marks on its input with the restriction that only a bounded number of these marks can exist at any given time. An improvement of picture recognizability of the finite automaton is the reason why the multi-marker automaton was introduced. On the other hand, a multi-inkdot automaton is a conventional automaton capable of dropping an inkdot on a given input tape for a landmark, but unable to further pick it up. This paper deals with marker versus inkdot over threedimensional input tapes, and investigates some properties.

Dynamic neighbourhood cellular automata

Abstract: We propose a defi nition of Cellular Automaton in which links between cells can change during the computation. This is done locally by each cell, which can reach the neighbours of its neighbours in a single computational step. We suggest that Dynamic Neighbourhood Cellular Automata can serve as a theoretical model for studying Algorithmic and Computational Complexity issues in the are of Ubiquitous Computing. We illustrate this approach by giving an optimal logarithmic time solution of the Firing Squad Synchronisation problem in our model, which is an exponential speed-up over classical Cellular Automata.

A Construction Method of Moore Neighborhood Number-Conserving Cellular Automata

Abstract: A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total of the numbers (states) of all cells of a global configuration is conserved throughout its computing process. It can be thought to be a kind of modelization of the physical conservation law of mass or energy. In this paper, we show a sufficient condition for a Moore neighborhood CA to be number-conserving. According to this condition, the local function of rotation-symmetric NCCA is expressed by a summation of quaternary functions. On this framework, we construct a 6-state logically universal NCCA.

Induced Subshifts and Cellular Automata

Abstract: Given a shift subspace over a finitely generated group, we define the subshift induced by it on a larger group. Then we do the same with cellular automata and, while observing that the new automaton can model a different abstract dynamics, we remark several properties that are shared with the old one. After that, we simulate the old automaton inside the new one, and discuss some consequences and restrictions.

Estimating the latent time of fault detection in finite automaton tested in real time

Abstract: The notions of potential and real latent times of fault detection in finite automata were introduced. The potential latent time is the minimal theoretical time of automaton fault detection, the real time is defined as the time of fault manifestation at a certain point. A method for determination of the statistical characteristics of both times for the automaton tested in the course of its real operation was proposed. It is based on selection of the trajectories of the Markov chain describing behavior of the operable and faulty automata. Additionally, a method for determination of the upper bound of the mean latent time in the case of limited information about the automaton characteristics was proposed.

A Recursive Padding Technique on Nondeterministic Cellular Automata

Abstract: We present a tight time-hierarchy theorem for nondeterministic cellular automata by using a recursive padding argument. It is shown that, if t2(n) is a time-constructible function and t2(n) grows faster than t1(n + 1), then there exists a language which can be accepted by a t2(n)-time nondeterministic cellular automaton but not by any t1(n)-time nondeterministic cellular automaton.