The Church problem for expansions of (N,<) by unary predicates
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A parameterized version of the Church synthesis problem, in this extended version a formula B and a finite-state operator F might contain as a parameter a unary predicate P, such that the Church problem with the parameter P is decidable.Abstract:
For a two-variable formula B(X,Y) of Monadic Logic of Order (MLO) the Church synthesis problem concerns the existence and construction of a finite-state operator Y=F(X) such that B(X,F(X)) is universally valid over Nat. Buchi and Landweber (1969) proved that the Church synthesis problem is decidable. We investigate a parameterized version of the Church synthesis problem. In this extended version a formula B and a finite-state operator F might contain as a parameter a unary predicate P. A large class of predicates P is exhibited such that the Church problem with the parameter P is decidable. Our proofs use composition method and game theoretical techniques.read more
Citations
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Book ChapterDOI
Monadic Second-Order Logic with Arbitrary Monadic Predicates
TL;DR: It is shown that Monadic Second-Order Logic defines a class of languages that has algebraic, automata-theoretic and machine-independent characterizations and the regularity question is considered: given a language in this class, when is it regular?
Posted Content
Monadic Second-Order Logic with Arbitrary Monadic Predicates
TL;DR: In this article, the authors study monadic second-order logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates, and show that it defines a class of languages that have algebraic, automata-theoretic and machine-independent characterizations.
Journal ArticleDOI
Monadic Second-Order Logic with Arbitrary Monadic Predicates
TL;DR: It is shown that Monadic Second-Order Logic defines a class of languages that has algebraic, automata-theoretic, and machine-independent characterizations and the regularity question is considered: Given a language in this class, when is it regular?
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The first order properties of products of algebraic systems
Solomon Feferman,R. L. Vaught +1 more
Book
Infinite Words: Automata, Semigroups, Logic and Games
Dominique Perrin,Jean-Eric Pin +1 more
TL;DR: The first manual devoted to Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words.