Showing papers on "Continuous automaton published in 2006"
25 Sep 2006
TL;DR: The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministicAutomata are constructed that omit the determinization step in game solving and reactive synthesis.
Abstract: The synthesis of reactive systems requires the solution of two-player games on graphs with ω-regular objectives. When the objective is specified by a linear temporal logic formula or nondeterministic Buchi automaton, then previous algorithms for solving the game require the construction of an equivalent deterministic automaton. However, determinization for automata on infinite words is extremely complicated, and current implementations fail to produce deterministic automata even for relatively small inputs. We show how to construct, from a given nondeterministic Buchi automaton, an equivalent nondeterministic parity automaton $\ensuremath {\cal P}$ that is good for solving games with objective $\ensuremath {\cal P}$. The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministic automaton. In this way, we omit the determinization step in game solving and reactive synthesis. The fact that our automata are nondeterministic makes them surprisingly simple, amenable to symbolic implementation, and allows an incremental search for winning strategies.
122 citations
TL;DR: This work provides a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions, and shows promise are computational elements.
Abstract: Rule 54, a two state, three neighbor cellular automaton in Wolfram’s systems of nomenclature, is less complex that Rule 110, but nevertheless possess a rich and complex dynamics. We provide a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions. Many of them shows promise are computational elements.
74 citations
TL;DR: It is shown how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton.
Abstract: A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space–time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton.
58 citations
TL;DR: An adaptive random search method based on continuous action-set learning automaton for solving stochastic optimization problems in which only the noise-corrupted value of function at any chosen point in the parameter space is available.
Abstract: In this paper, we study an adaptive random search method based on continuous action-set learning automaton for solving stochastic optimization problems in which only the noise-corrupted value of function at any chosen point in the parameter space is available. We first introduce a new continuous action-set learning automaton (CALA) and study its convergence properties. Then we give an algorithm for optimizing an unknown function.
51 citations
TL;DR: Employing the structure theorem for quantum cellular automata, a general construction scheme is given to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models.
Abstract: We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models. We use this technique to construct a universally programmable cellular automaton on a one-dimensional lattice with single cell dimension 12.
49 citations
20 Sep 2006
TL;DR: The improvement comprises at least one observation window positioned in the upper hemisphere of the envelope in substitution for an envelope panel sufficient to permit an occupant of a balloon carriage suspended from the envelope to look upwardly through the bottom opening and the observation window to view large objects, such as other balloons in the vicinity above the balloon envelope.
Abstract: A Cellular Automaton (CA) describing a predator–prey dynamics is proposed This model is fully local, i.e., without any “spurious” Monte Carlo step during the movement phase A particular attention has been addressed to the comparison of the obtained simulations with the discrete version of the Lotka–Volterra equations.
23 citations
Journal Article•
TL;DR: It is demonstrated that the rich spatio-temporaldynamics of interacting traveling localizations and their generators can be used to implement computation, namely manipulation with signals, binary logical operations, multiple-value operations, and finite-state ma-chines.
Abstract: A hexagonal ternary-state two-dimensional cellular automaton is de-signed which imitates an activator-inhibitor reaction-diffusion system,where the activator is self-inhibited in particular concentrations and theinhibitor dissociates in the absence of the activator. The automaton ex-hibits both stationary and mobile localizations (eaters and gliders), andgenerators of mobile localizations (glider-guns). A remarkable feature ofthe automaton is the existence of spiral glider-guns, a discrete analog of aspiral wave that splits intolocalizedwave-fragments (gliders) at some dis-tance from the spiral tip. It is demonstrated that the rich spatio-temporaldynamics of interacting traveling localizations and their generators canbe used to implement computation, namely manipulation with signals,binary logical operations, multiple-value operations, and finite-state ma-chines.
22 citations
10 Jul 2006
TL;DR: This paper improves the construction of deterministic asynchronous automata from finite state automaton, and improves the well-known construction in that the size of the asynchronous automaton is simply exponential in both the sizes of the sequential automaton and the number of processes.
Abstract: The well-known algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the well-known construction in that the size of the asynchronous automaton is simply exponential in both the size of the sequential automaton and the number of processes. In contrast, Zielonka's algorithm gives an asynchronous automaton that is doubly exponential in the number of processes (and simply exponential in the size of the automaton)
22 citations
Journal Article•
TL;DR: In this article, the authors improved the construction of deterministic asynchronous automata from finite state automata and gave an asynchronous automaton that is doubly exponential in both the number of processes and the size of the automaton.
Abstract: The well-known algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the well-known construction in that the size of the asynchronous automaton is simply exponential in both the size of the sequential automaton and the number of processes. In contrast, Zielonka's algorithm gives an asynchronous automaton that is doubly exponential in the number of processes (and simply exponential in the size of the automaton).
22 citations
Journal Article•
TL;DR: The problem of constructing fine automata for general safety LTL formulas was left open by Kupferman and Vardi as mentioned in this paper, who showed that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of the fine automaion is still only exponential in the length of the formula.
Abstract: Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verification can be reduced to reasoning about finite words: a system is correct if none of its computations has a bad prefix. Checking the latter circumvents the need to reason about cycles and simplifies significantly methods like symbolic fixed-point based verification, bounded model checking, and more. A drawback of the translation lies in the size of the automata: while the translation of a safety LTL formula ψ to a nondeterministic Biichi automaton is exponential, its translation to a tight bad-prefix automaton - one that accepts all the bad prefixes of ψ, is doubly exponential. Kupferman and Vardi showed that for the purpose of verification, one can replace the tight automaton by a fine automaion - one that accepts at least one bad prefix of each infinite computation that violates ψ. They also showed that for many safety LTL formulas, a fine automaton has the same structure as the Buchi automaton for the formula. The problem of constructing fine automata for general safety LTL formulas was left open. In this paper we solve this problem and show that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of a fine automaton is still only exponential in the length of the formula.
21 citations
23 Oct 2006
TL;DR: The problem of constructing fine automata for general safety LTL formulas was left open and it is shown that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of afine automaton is still only exponential in the length of the formula.
Abstract: Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verification can be reduced to reasoning about finite words: a system is correct if none of its computations has a bad prefix. Checking the latter circumvents the need to reason about cycles and simplifies significantly methods like symbolic fixed-point based verification, bounded model checking, and more.
A drawback of the translation lies in the size of the automata: while the translation of a safety LTL formula ψ to a nondeterministic Buchi automaton is exponential, its translation to a tight bad-prefix automaton — one that accepts all the bad prefixes of ψ, is doubly exponential. Kupferman and Vardi showed that for the purpose of verification, one can replace the tight automaton by a fine automaton — one that accepts at least one bad prefix of each infinite computation that violates ψ. They also showed that for many safety LTL formulas, a fine automaton has the same structure as the Buchi automaton for the formula. The problem of constructing fine automata for general safety LTL formulas was left open. In this paper we solve this problem and show that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of a fine automaton is still only exponential in the length of the formula.
TL;DR: An equilibrium synchronous network of cells highly sensitive to the state of their neighborhood and able to capture the effects of confinement by means of few flexible local parameters and a parallel, local evolution rule is constructed.
Abstract: Topological constraints play a fundamental role in problems involving the transfer of heat, matter, or information in a discrete network. Flows in microporous media are the most common cases in which the thermodynamic and transport properties of adsorbate are strongly influenced by its interactions with the confining medium. Combining two local Monte Carlo operations and a Lattice-Gas Cellular Automaton, we constructed an equilibrium synchronous network of cells highly sensitive to the state of their neighborhood and able to capture the effects of confinement by means of few flexible local parameters and a parallel, local evolution rule. Results of an application of the model to the specific problem of geometrical restricted long-range diffusion are used to interpret the behaviors of particles in tight confinement.
TL;DR: The reversibility problem for 150 Wolfram cellular automata is tackled for null boundary conditions and it is explicitly shown that the reversibility depends on the number of cells of the cellular automaton.
Abstract: In this paper, the reversibility problem for 150 Wolfram cellular automata is tackled for null boundary conditions. It is explicitly shown that the reversibility depends on the number of cells of the cellular automaton. The inverse cellular automaton for each case is also computed.
TL;DR: Deterministic logical-dynamical systems are considered with the dynamical part described by differential equations and the logical part modeling the work of an automaton with memory is described by recursive inclusions.
Abstract: Deterministic logical-dynamical systems are considered with the dynamical part described by differential equations. The logical part modeling the work of an automaton with memory is described by recursive inclusions. Sufficient optimality conditions are obtained for the construction of the logical (automaton) part of the logical-dynamical system.
ETSI1
TL;DR: The effect of simple memory (memory in cells and links) on a particular reversible, structurally dynamic cellular automaton in the hexagonal tessellation is explored in this paper.
Abstract: The major features of conventional cellular automata include the inalterability of topology and the absence of memory The effect of simple memory (memory in cells and links) on a particular reversible, structurally dynamic cellular automaton in the hexagonal tessellation is explored in this paper.
17 Jul 2006
TL;DR: This new automaton, called IJA, is an improvement of the Krinsky FSSA and not only ε-optimal and expedient, but also converges to the optimal action faster than the old one.
Abstract: In this paper, we present a new fixed structure learning automaton (FSSA), called IJA, and study its steady state behavior in stationary environments. The proposed automaton characterizes by star shaped transition diagram and each branch of the star contains N states associated with a particular action. This new automaton is an improvement of the Krinsky FSSA and not only e-optimality and expedient, but also converges to the optimal action faster than the old one.
01 Dec 2006
TL;DR: The notion of finite time mode abstraction is introduced to relate a hybrid automaton to a timed automaton that preserves the stability and reachability properties of the former and a new notion of hybrid distance metric is introduced.
Abstract: In this paper we introduce the notion of Finite Time Mode Abstraction to relate a hybrid automaton to a timed automaton that preserves the stability and reachability properties of the former. The abstraction procedure discards the continuous dynamics of each mode in the hybrid automaton completely, keeping only the information about the maximum time in which the continuous state makes a discrete jump. This information is used to construct a timed automaton, based on the original hybrid automaton, and to prove that the stability and reachability properties of the original system are retained in the abstract timed automaton. In the process of abstracting a hybrid to a timed automaton we introduce a new notion of hybrid distance metric, which provides information about both the number of discrete transitions that a system would have to make to go from one hybrid state to another, and the distance between the continuous parts of such hybrid states.
TL;DR: A control synthesis method for discrete event systems whose behavior is dependent on explicit values of time is introduced, which consists in computing new firing conditions for the timed automaton transitions so that the forbidden locations are no longer reachable.
01 Aug 2006
TL;DR: In this paper, it was shown that there is an infinite strict double-dimensional-bit hierarchy for one-dimensional iterative arrays and for two-way cellular automata with inter-cell communication restricted to a constant number of bits independent of the number of states.
Abstract: A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. The distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as a p |p prim or a 2n |n∈ℕ [16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite different from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.
TL;DR: Estimates of the minimal number of states of an automaton able to control a given automaton are found and it is proved that, on average, feedback closed-loop control automata do not have fewer states than open-loopcontrol automata when the control objective is to steer the controlled automaton to a target state.
Abstract: We consider control questions for finite automata viewed as input/output systems. In particular, we find estimates of the minimal number of states of an automaton able to control a given automaton. We prove that, on average, feedback closed-loop control automata do not have fewer states than open-loop control automata when the control objective is to steer the controlled automaton to a target state. We compare our approach to other ways of formalizing of formalizing analogous control objectives.
TL;DR: This work gives a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete analogue of the source term.
Abstract: Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete analogue of the source term This new representation is general, but not unique, and can be used to represent, in a more visual way, any one-dimensional cellular automaton rule A few illustrative examples are presented
TL;DR: Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata for the suppression of phase transitions and the relevance of detailed balance of the resulting probabilism cellular automaton for the critical behavior is pointed out.
Abstract: Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.
Journal Article•
Journal Article•
TL;DR: This survey paper reviews the means that allow to go from one representation of the languages to the other and how, and to what extend, one can keep them small.
Abstract: This survey paper reviews the means that allow to go from one representation of the languages to the other and how, and to what extend, one can keep them small. Some emphasis is put on the comparison between the expressions that can be computed from a given automaton and on the construction of the derived term automaton of an expression.
TL;DR: This paper proposes a universal constructor implemented on a self-timed cellular automaton, which is a particular type of asynchronous Cellular automaton that employs 39 rotation-invariant rules and the state of each cell is encoded by 8 bits.
Abstract: This paper proposes a universal constructor implemented on a self-timed cellular automaton, which is a particular type of asynchronous cellular automaton. Our construction utilizes the asynchronous nature of the underlying cellular automaton in a direct way, as a result of which it is simpler than the conventional construction based on the simulation of a synchronous cellular automaton by an asynchronous cellular automaton. Our model employs 39 rotation-invariant rules and the state of each cell is encoded by 8 bits.
TL;DR: The kinetics of damage accumulation and the evolution of damage clusters in loaded materials are simulated with a probabilistic cellular automaton controlled by three probabilities, namely, by the probabilities of free-cell occupation, cluster perimeter growth, and coalescence of clusters separated by a critical distance.
Abstract: The kinetics of damage accumulation and the evolution of damage clusters in loaded materials are simulated with a probabilistic cellular automaton controlled by three probabilities, namely, by the probabilities of free-cell occupation, cluster perimeter growth, and coalescence of clusters separated by a critical distance. The automaton algorithm is realized with Microsoft Visual Basic 6.0 as a single-document Windows application connected with Microsoft Excel, which is used as an automaton client to save and process output data. The operation of the automaton is illustrated by the example of the kinetics of damage accumulation and the evolution of a damage cluster structure compared for two simulation scenarios.
Journal Article•
TL;DR: The main result of the paper establishes the presence of local nested structure in k-color rules with this bijectivity property, and explores a class of integer sequences characterizing the nested structure.
Abstract: At row 2n in the cellular automaton rule 30, a region of the initial condition reappears on the right side, which causes the automaton to “begin again” locally. As a result, local nested structure is produced. This phenomenon is ultimately due to the property that rule 30 is reversible in time under the condition that the right half of each row is white. The main result of the paper establishes the presence of local nested structure in k-color rules with this bijectivity property, and we explore a class of integer sequences characterizing the nested structure. We also prove an observation of Wolfram regarding the period length doubling of diagonals on the left side of rule 30.
TL;DR: An approach to studying such systems that is based on set-theoretical and topological constructs is considered and results of application of this approach to some binary cellular automata are given.
Abstract: On the one hand, a system of discrete relations is a generalization of cellular automaton and, on the other hand, it is a set-theoretical analog of a system of polynomial equations. An approach to studying such systems that is based on set-theoretical and topological constructs is considered. The proposed approach is implemented as a C program. Results of application of this approach to some binary cellular automata are given. In the binary case, cellular automata can be represented by systems of polynomial equations, which are normally studied by the Grobner basis method. Our approach is compared with this method on some examples.
29 Nov 2006
TL;DR: Two single pattern matching algorithms are presented, each of which is composed by a smallest suffix automaton and a forward finite state automaton, which show that the average time complexities of two algorithms are less than that of RF and LDM for short patterns and that of BM for long patterns over small alphabets or short lengths over large alphabs.
Abstract: In this paper, two single pattern matching algorithms are presented, each of which is composed by a smallest suffix automaton and a forward finite state automaton. Whatever the suffix automaton or the forward finite state automaton is running, the window shifts m-R characters and then the suffix automaton starts running if no pattern prefix is found (R is zero) in the first algorithm or R is not greater than half of m in the second algorithm, otherwise, the forward finite state automaton starts running. Their time complexities are all O(n) in the worst case and O(n/m) in the best case. The experimental results show that the average time complexities of two algorithms are less than that of RF and LDM for short patterns and that of BM for long patterns over small alphabets or short lengths over large alphabets.
16 Oct 2006
TL;DR: A sequence generation problem on a special restricted class of cellular automata having 1-bit inter-cell communications (CA1-bit) is studied and several state-efficient real-time sequence generation algorithms for non-regular sequences are proposed.
Abstract: Cellular automata (CA) are considered to be a non-linear model of complex systems in which an infinite one-dimensional array of finite state machines (cells) updates itself in a synchronous manner according to a uniform local rule. We study a sequence generation problem on a special restricted class of cellular automata having 1-bit inter-cell communications (CA1-bit) and propose several state-efficient real-time sequence generation algorithms for non-regular sequences.