Model Checking Languages of Data Words

Overview & Synopsis

We consider the model-checking problem for data multi-pushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.