MSO-Definable Regular Model Checking

Regular Model Checking (RMC) is a symbolic model checking technique where the set of system states are expressed as regular languages over strings and the transition relation is expressed using rational string-to-string relations. RMC permits verification of non-trivial properties in systems with infinite state spaces. We introduce monadic second-order logic (MSO) definable regular model checking (MSO-RMC), a framework that generalizes RMC by enabling the modeling of systems with more complex transition relations which are definable using nondeterministic MSO-definable string-to-string transformations. While MSO-RMC is in general undecidable, we recover decidability of the bounded model checking problem within this framework. For this decidability result, we introduce nondeterministic streaming $\omega$-string transducers and establish their expressive equivalence to nondeterministic MSO-definable $\omega$-string transformations. We also proof of the decidability of the regular type checking problem for nondeterministic streaming string transducers, both in the setting of finite strings and $\omega$-strings. Since MSO-definable relations are closed under composition, this result implies decidability of the bounded model checking in MSO-RMC.