Model Checking Concurrent Recursive Programs Using Temporal Logics

Abstract

We consider two bounded versions of the model checking problem of a fixed temporal logic $\textrm{TL}$ whose modalities are MSO-definable and which is specifying properties of multiply nested words, i.e., of runs of pushdown automata with multiple stacks. One of the problems asks, given a multi-stack system $\mathcal{A}$, a temporal formula F from $\textrm{TL}$, and a bound k, whether all nested words ν which are accepted by $\mathcal{A}$ and whose split-width is bounded by k satisfy F. We describe the connection between the complexity of this problem and the maximal number n of monadic quantifier alternations in the definitions of the modalities of $\textrm{TL}$. In fact, we present almost tight upper and lower bounds for every natural number n. Regarding the other model checking problem considered, we require ν to be a k-scope nested word. In this case, we can infer the same lower and upper bounds.