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Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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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.
19 citations
TL;DR: It is shown 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.
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.
19 citations
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.
19 citations
TL;DR: The simulations show that the average transient time Tave increases algebraically with system size N, Tave∼Nα, with α≈1.08, and that the density of propagating objects (gliders) decays with time as ngl∼-γ with γ≈0.64.
19 citations
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.
19 citations