Journal ArticleDOI
A property of the Schützenberger product
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This article is published in Semigroup Forum.The article was published on 1986-12-01. It has received 13 citations till now. The article focuses on the topics: Syntactic monoid & Trace theory.read more
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Syntactic semigroups
TL;DR: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad, or from public or private research centers.
Journal ArticleDOI
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.
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A survey on small fragments of first-order logic over finite words
TL;DR: The algebraic approach is used to show decidability of expressibility within fragments of first-order logic over finite words and to give a proof of Simon's theorem on factorization forests restricted to aperiodic monoids.
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Some results on the dot-depth hierarchy
TL;DR: In this article, a lower bound for the dot-depth of an aperiodic monoid is given, and the equality of two decidable varieties which were known to contain all dot depth two monoids is shown.
References
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Automata, Languages, and Machines
TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.
Journal ArticleDOI
Characterizations of locally testable events
Janusz A. Brzozowski,Imre Simon +1 more
TL;DR: LT events and k-testable events are characterized in terms of restricted star-free expressions based on finite and cofinite events; finite automata accepting these events; (c) semigroups; and (d) structural decomposition of such automata.
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A generalization of the Schützenberger product of finite monoids
TL;DR: As an application of the generalized product, the theorem of Brzozowski and Knast that the dot-depth hierarchy of star-free sets is infinite is proved.
Journal ArticleDOI
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.