Topic

# Deterministic automaton

About: Deterministic automaton is a research topic. Over the lifetime, 2734 publications have been published within this topic receiving 62537 citations.

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.

Abstract: Alur, R. and D.L. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235. We propose timed (j&e) automata to model the behavior of real-time systems over time. Our definition provides a simple, and yet powerful, way to annotate state-transition graphs with timing constraints using finitely many real-valued clocks. A timed automaton accepts timed words-infinite sequences in which a real-valued time of occurrence is associated with each symbol. We study timed automata from the perspective of formal language theory: we consider closure properties, decision problems, and subclasses. We consider both nondeterministic and deterministic transition structures, and both Biichi and Muller acceptance conditions. We show that nondeterministic timed automata are closed under union and intersection, but not under complementation, whereas deterministic timed Muller automata are closed under all Boolean operations. The main construction of the paper is an (PSPACE) algorithm for checking the emptiness of the language of a (nondeterministic) timed automaton. We also prove that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the nondeterministic case and PSPACE-complete in the deterministic case. Finally, we discuss the application of this theory to automatic verification of real-time requirements of finite-state systems.

7,096 citations

••

TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.

Abstract: Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.

1,930 citations

••

01 Jan 1971

TL;DR: An algorithm is given for minimizing the number of states in a finite automaton or for determining if two finite automata are equivalent and the running time is bounded by k n log n.

Abstract: An algorithm is given for minimizing the number of states in a finite automaton or for determining if two finite automata are equivalent. The asymptotic running time of the algorithm is bounded by k n log n where k is some constant and n is the number of states. The constant k depends linearly on the size of the input alphabet.

898 citations

••

TL;DR: The critical state is characterized, and its entropy for an arbitrary finite lattice in any dimension is determined, and the two-point correlation function is shown to satisfy a linear equation.

Abstract: We study a general Bak-Tang-Wiesenfeld--type automaton model of self-organized criticality in which the toppling conditions depend on local height, but not on its gradient. We characterize the critical state, and determine its entropy for an arbitrary finite lattice in any dimension. The two-point correlation function is shown to satisfy a linear equation. The spectrum of relaxation times describing the approach to the critical state is also determined exactly.

856 citations

••

TL;DR: The question of whether there is an automaton with n states which agrees with a finite set D of data is shown to be NP-complete, although identification-in-the-limit of finite automata is possible in polynomial time as a function of the size of D.

Abstract: The question of whether there is an automaton with n states which agrees with a finite set D of data is shown to be NP-complete, although identification-in-the-limit of finite automata is possible in polynomial time as a function of the size of D. Necessary and sufficient conditions are given for D to be realizable by an automaton whose states are reachable from the initial state by a given set T of input strings. Although this question is also NP-complete, these conditions suggest heuristic approaches. Even if a solution to this problem were available, it is shown that finding a minimal set T does not necessarily give the smallest possible T.

819 citations