Characterizations of some classes of regular events
TLDR
Two special classes of regular events are studied: the piecewise testable events and the events of dot-depth one, especially in terms of their minimal automaton.About:
This article is published in Theoretical Computer Science.The article was published on 1985-01-01 and is currently open access. It has received 64 citations till now. The article focuses on the topics: Piecewise.read more
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Book ChapterDOI
CHAPTER 1 – Finite Automata
TL;DR: The field of finite automata is a branch of mathematics connected with the algebraic theory of semigroups and associative algebras as discussed by the authors, which is one of the most important areas of automata research.
Book
Syntactic semigroups
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Polynomial closure and unambiguous product
Jean-Eric Pin,Pascal Weil +1 more
TL;DR: It is shown that if a language and its complement are in the polynomial closure of a variety of languages, then this language can be written as a disjoint union of marked unambiguous products of languages of the variety.
Journal ArticleDOI
Complexity of some problems from the theory of automata
TL;DR: The complexity of three problems, namely star-free events, events of dot-depth one and piecewise testable events, are investigated in the style of (Garey and Johnson, 1979).
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Logic, semigroups and automata on words
TL;DR: A survey article on the connections between the “sequential calculus” of Büchi, a system which allows to formalize properties of words, and the theory of automata, which includes some very recent results on the algebraic theory of infinite words.
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Journal ArticleDOI
On finite monoids having only trivial subgroups
TL;DR: An alternative definition is given for a family of subsets of a free monoid that has been considered by Trahtenbrot and by McNaughton.
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Classifying regular events in symbolic logic
TL;DR: It is shown that the natural classification of events depending on these quantifiers will not yield on infinite hierarchy, and that the latter two hierarchies have appealing characterizations in symbolic logic.
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Dot-depth of star-free events
TL;DR: The use of two-sided quotients adds insight to the theory of star-free events and permits the derivation of some new properties of these events; in particular, every star- free event has at least one quotient which is either empty or full.
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A semigroup characterization of dot-depth one languages
TL;DR: It is shown that one can décide whether a langage has dot-depth one in thedot-depth hierarchy introduced by BrzozowskL based on an algebraic characterization of the syntactic semigroup of a langages of dot- depth 0 or 1.