The Temporal Logic of Reactive and Concurrent Systems: Specification

General Topology-I

Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.

Automata on infinite objects

The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

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Languages, automata, and logic

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

On a conjecture of Rhodes

https://hal.archives-ouvertes.fr/hal-00018556/document

Sur le monoide syntactique de L∗ lorsque L est un langage fini

The aim of this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or ∑n-hierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive power of the lower levels was not characterized effectively. We give a semigroup theoretic description of the expressive power of ∑1, the existential formulas, and s∑1, the boolean combinations of existential formulas. Our characterization is algebraic and makes use of the syntactic semigroup, but contrary to a number of results in this field, is not in the scope of Eilenberg's variety theorem, since se1-definable languages are not closed under residuals.

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The Expressive Power of Existential First Order Sentences of Büchi's Sequential Calculus

We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived semigroupoid theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of J-trivial monoids constitute local varieties, and we derive some decomposition theorems from these results.

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Ordered categories and ordered semigroups

Carrying on the work of Arnold, Pecuchet and Perrin, Wilke has obtained a counterpart of Eilenberg's variety theorem for finite and infinite words. In this paper, we extend this theory for classes of languages that are closed under union and intersection, but not necessarily under complement. As an example, we give a purely algebraic characterization of various classes of recognizable sets defined by topological properties (open, closed, F ∑ and F δ ) or by combinatorial properties

/pdf/positive-varieties-and-infinite-words-14lxyyk26s.pdf

Jean-Eric Pin

Papers

On a conjecture of Rhodes

Sur le monoide syntactique de L∗ lorsque L est un langage fini

The Expressive Power of Existential First Order Sentences of Büchi's Sequential Calculus

Ordered categories and ordered semigroups

Positive Varieties and Infinite Words