Section: New Results

Model checking languages over infinite alphabets

In [61] , we consider data words, i.e, strings where each position carries both a label from a finite alphabet and some values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that data words are suitable to model the behavior of a concurrent program with dynamic process creation. A variety of formalisms, including logic and automata, have been studied in the literature to specify sets of data words in the context of verification. Most of them focus on the satisfiability problem of very restricted logics, as the general problem is undecidable.

Here, we consider the dual approach of restricting the domain of data words instead of pruning the logic. This allows us to tackle the model-checking problem with respect to monadic second-order (MSO) properties. As model checking is undecidable for nearly all known automata models (including the model presented in the first part of the talk), we introduce data pushdown automata (DPA). DPA come with multiple pushdown stacks (where the access to stacks is bounded by a number of phase switches) and are enriched with parameters that can be instantiated with data values. DPA can model interesting protocols like a leader election protocol with an unknown number of processes. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), we show that one can decide if all words generated by a DPA satisfy a given formula from the full MSO logic.