J.-E. Pin. Semigroups and Automata on Words. Annals Mathematics & AI, 16:343--384, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....detailed in sections 7 and 11. The other partial results concerning these hierarchies are briefly reviewed in section 11. Another remarkable fact about these hierarchies is their connections with some hierarchies of formal logic. See the article of W. Thomas in this volume or the survey article [41]. But it is time for us to hark back to Schutzenberger s theorem on star free sets. 6. Star free languages The set of star free subsets of A is the smallest set of subsets of A containing the finite sets and closed under finite boolean operations and product. For instance, is star free, ....

J.-E. Pin, Logic, Semigroups and Automata on Words, Proceedings of the Spring School on Logic and Computer Science, ed. S. Grigorieff, to appear.

....in [Lad77] The ideas can also be generalized to second order sentences to obtain another proof of B uchi s theorem for words of length less than n . Syntactic semigroups and logics over nite and words have been widely studied to obtain hierarchies over rational languages (see for example [Pin96]) This can also be generalized to words of length less than n . Finally, we introduced in [Bed98b, BC98] an algebraic structure adapted to the study of words of any denumerable length. The main theorem of this paper (theorem 45) is extended to sets of words of denumerable length in [Bed] ....

Jean-Eric Pin. Logic, semigroups and automata on words. Ann. Math. Articial Intelligence, 16(1-4):343-384, 1996.

....also link pseudovarieties to other domains of mathematics and computer science: twenty years after Eilenberg s theorem, fruitful correspondences between nite semigroups, rational languages, rst order logic, second order monadic logic and temporal logic still motivate intensive work. See [13, 14, 19, 20, 21] for di erent presentations of these relationships. Pseudovarieties are frequently de ned by means of unary or binary operators. Three of these operators, the join, the semidirect product and the Mal cev product do not preserve decidability: Albert, Baldinger and Rhodes [1] exhibited two decidable ....

Jean-  Eric Pin. Logic, semigroups and automata on words. Ann. Math. Artif. Intel., 16:343-384, 1996.

....a characterization in terms of ESO prefix classes is impossible. McNaughton and Papert [25] showed that FOL with a linear order captures the star free regular languages, which was extended to languages by Thomas [37] Also hierarchies of star free languages were logically characterized, see e.g. [37, 28, 29, 30]. Straubing, Th erien and Thomas [35] showed that FOL with modular counting quantifiers captures the regular languages whose syntactic monoids contain only solvable groups; see [34, 37, 28, 29, 30] for these and related results. 2 Preliminaries We consider second order logic with equality and ....

.... by Thomas [37] Also hierarchies of star free languages were logically characterized, see e.g. 37, 28, 29, 30] Straubing, Th erien and Thomas [35] showed that FOL with modular counting quantifiers captures the regular languages whose syntactic monoids contain only solvable groups; see [34, 37, 28, 29, 30] for these and related results. 2 Preliminaries We consider second order logic with equality and without function symbols of positive arity. Predicates are denoted by capitals and individual variables by lower case letters; a bold face version of a letter denotes a tuple of corresponding ....

J.-E. Pin. Semigroups and Automata on Words. Annals Mathematics & AI, 16:343--384, 1996.

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J.-E. Pin, Logic, Semigroups and Automata on Words, Proceedings of the Spring School on Logic and Computer Science, ed. S. Grigorieff, to appear.

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J.-E. Pin, Logic, Semigroups and Automata on Words, Theor. Comp. Sc., to appear.

....model the behaviour of programs or circuits. From a mathematical point of view, they have a rich structure, at the cross roads of logic, topology and algebra. This paper emphasizes the combinatorial and algebraic aspects of this theory but the interested reader is referred to the survey articles [32,43] or to the report [30] for more information on the other aspects. In particular, the important topic of the complexity of the algorithms on infinite words is not treated in this paper. The paper is written with the perspective of generalizing the results on recognizable sets of finite words to ....

J.-E. Pin, Logic, Semigroups and Automata on words, to appear.

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J.-E. Pin. Semigroups and Automata on Words. Annals Mathematics & AI, 16:343--384, 1996.

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