Monadic Second-Order Logic with Arbitrary Monadic Predicates

Nathanaël Fijalkow (1) , Charles Paperman (2, 3)

1 University of Oxford
2 LINKS - Linking Dynamic Data
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic, and machine-independent characterizations. We consider the regularity question: Given a language in this class, when is it regular? To answer this, we show a substitution property and the existence of a syntactical predicate. We give three applications. The first two are to give very simple proofs that the Straubing Conjecture holds for all fragments of MSO with monadic predicates and that the Crane Beach Conjecture holds for MSO with monadic predicates. The third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.

Mots clés: Automata with Advice; Monadic Predicates; Morphic Predicates

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]; Complexité [cs.CC]

Nathanaël Fijalkow, Charles Paperman. Monadic Second-Order Logic with Arbitrary Monadic Predicates. ACM Transactions on the Web, 2017, 9 (3), pp.39 - 56. ⟨10.1145/3091124⟩. ⟨hal-01587624⟩