The theory of reachability in trace-pushdown systems
For researchers in formal verification and automata theory, this extends the decidability frontier for reachability in systems with concurrency and stack-like behavior.
The paper identifies a class of trace-pushdown systems for which the first-order theory of their configuration graph with reachability is decidable, complementing prior work that required severe restrictions on the dependence alphabet.
We consider pushdown systems that store, instead of a single word, a Mazurkiewicz trace on its stack. These systems are special cases of valence automata over graph monoids and subsume multi-stack systems. We identify a class of such systems that allow to decide the first-order theory of their configuration graph with reachability. This result complements results by D'Osualdo, Meyer, and Zetzsche (namely the decidability for arbitrary pushdown systems under a severe restriction on the dependence alphabet).