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Quantum finite automata
About: Quantum finite automata is a research topic. Over the lifetime, 3725 publications have been published within this topic receiving 96542 citations.
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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.
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
Book•
01 Mar 1988TL;DR: Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines
Abstract: Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial composition of automata The parallel decomposition theorem The serial decomposition theorem The lattice of SP partitions Analysis of machines Concurrent systems: net theory Concurrent systems: the calculus of communicating systems. Appendix: Sets, relations and functions.
1,582 citations
02 Jan 1991
TL;DR: This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree.
Abstract: Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.
1,475 citations
TL;DR: The formalism of regular expressions was introduced by S. C. Kleene to obtain the following basic theorems.
Abstract: The formalism of regular expressions was introduced by S. C. Kleene [6] to obtain the following basic theorems.
1,132 citations