Descriptional and computational complexity of finite automata—A survey

Finite automata are probably best known for being equivalent to right-linear context-free grammars and, thus, for capturing the lowest level of the Chomsky-hierarchy, the family of regular languages. Over the last half century, a vast literature documenting the importance of deterministic, nondeterm...

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Bibliographic Details
Published in:Information and computation Vol. 209; no. 3; pp. 456 - 470
Main Authors: Holzer, Markus, Kutrib, Martin
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier Inc 01.03.2011
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Alternation
Applied sciences
Computational complexity
Computer science; control theory; systems
Descriptional complexity
Determinism
Exact sciences and technology
Finite automata
Miscellaneous
Nondeterminism
Survey
Theoretical computing
Determinism
Descriptional complexity
Survey
Alternation
Finite automata
Nondeterminism
Computational complexity
Linear grammar
Approximation
Computer theory
Language family
Deterministic automaton
Minimization
Finite automaton
Regular language
Non determinism
Non deterministic automaton
Simulation
Context free grammar
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:Finite automata are probably best known for being equivalent to right-linear context-free grammars and, thus, for capturing the lowest level of the Chomsky-hierarchy, the family of regular languages. Over the last half century, a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss developments relevant to finite automata related problems like, for example, (i) simulation of and by several types of finite automata, (ii) standard automata problems such as fixed and general membership, emptiness, universality, equivalence, and related problems, and (iii) minimization and approximation. We thus come across descriptional and computational complexity issues of finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2010.11.013