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On decidability of monadic logic of order over the naturals extended by monadic predicates
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Fields of logic and computation
On Monadic theories of monadic predicates
Fields of logic and computation
Regular sets over extended tree structures
Theoretical Computer Science
Church synthesis problem with parameters
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Decidable theories of the ordering of natural numbers with unary predicates
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FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
The Church problem for expansions of (N,
Information and Computation
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We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures {N, , P} which expand the ordering {N, } of the natural numbers by a unary predicate P; the corresponding infinite word is the characteristic 0-1-sequence xp of P. We show that for a morphic predicate P the associated monadic second-order theory MTh{N, , P) is decidable, thus extending results of Elgot and Rabin (1966) and Maes (1999). The solution is obtained in the framework of semigroup theory, which is then connected to the known automata theoretic approach of Elgot and Rabin. Finally, a large class of predicates P is exhibited such that the monadic theory MTh(N, , P) is decidable, which unifies and extends the previously known examples.