Handbook of theoretical computer science (vol. B)
Open questions around Bu¨chi and Presburger arithmetics
Logic: from foundations to applications
An automota theoretic decidability proof for first-order theory of N, with morphic predicate P
Automatica (Journal of IFAC)
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Decision problems in buechi's sequential calculus
Decision problems in buechi's sequential calculus
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Decision Procedure for an Extension of WS1S
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Model Transformations in Decidability Proofs for Monadic Theories
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Decidable theories of the ordering of natural numbers with unary predicates
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
| Hi-index | 0.01 |
We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures (N, P) which expand the ordering (N, 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.