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# Two-way deterministic finite automaton

About: Two-way deterministic finite automaton is a research topic. Over the lifetime, 1409 publications have been published within this topic receiving 31026 citations.

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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

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01 Jan 1969

TL;DR: The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.

Abstract: From the Preface (See Front Matter for full Preface)
The study of formal languages constitutes an important subarea of computer science. This area sprang to life around 1956 when Noam Chomsky gave a mathematical model of a grammar in connection with his study of natural languages. Shortly afterwards, the concept of a grammar was found to be of great importance to the programmer when the syntax of the programming language ALGOL was defined by a context-free grammar. This development led naturally to syntax-directed compiling and the concept of a compiler compiler. Since then a considerable flurry of activity has taken place, the results of which have related formal languages and automata theory to such an extent that it is impossible to treat the areas separately. By now, no serious study of computer science would be complete without a knowledge of the techniques and results from language and automata theory.
This book presents the theory of formal languages as a coherent theory and makes explicit its relationship to automata. The book begins with an explanation of the notion of a finite description of a language. The fundamental descriptive device--the grammar--is explained, as well as its three major subclasses--regular, context-free, and context-sensitive grammars. The context-free grammars are treated in detail, and such topics as normal forms, derivation trees, and ambiguity are covered. Four types of automata equivalent to the four types of grammars are described. These automata are the finite automaton, the pushdown automaton, the linear bounded automaton, and the Turing machine. The Turing machine is covered in detail, and unsolvability of the halting problem shown. The book concludes with certain advanced topics in language theory--closure properties, computational complexity, deterministic pushdown automata, LR(k) grammars, stack automata, and decidability.

1,595 citations

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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

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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

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18 Jul 2001TL;DR: An algorithm to generate Buchi automata from LTL formulae is presented and compared with Spin: the experiments show that the algorithm is much more efficient than Spin.

Abstract: We present an algorithm to generate Buchi automata from LTL formulae. This algorithm generates a very weak alternating co-Buchi automaton and then transforms it into a Buchi automaton, using a generalized Buchi automaton as an intermediate step. Each automaton is simplified on-the-fly in order to save memory and time. As usual we simplify the LTL formula before any treatment. We implemented this algorithm and compared it with Spin: the experiments show that our algorithm is much more efficient than Spin. The criteria of comparison are the size of the resulting automaton, the time of the computation and the memory used. Our implementation is available on the web at the following address: http://verif.liafa.jussieu.fr/ltl2ba

725 citations