Well-Structured Pushdown Systems, Part 1: Decidable Classes for Coverability

Pushdown systems (PDSs) nicely model single-thread recursive programs, and well-structured transition systems (WSTS), such as vector addition systems, are useful to represent non-recursive multithread programs. Our goal is to investigate well-structured pushdown systems (WSPDSs), pushdown systems with well-quasi-ordered control states and stack alphabet, to combine these ideas. This paper focuses on decidable classes of coverability and extends Pautomata techniques for configuration reachability of PDSs to those for coverability of WSPDSs, in forward and backward ways. A Post^*-automata (resp. Pre^*-automata) construction is combined with Karp-Miller acceleration (resp. ideal representation) to characterize the set of successors (resp. predecessors) of given configurations. We show decidability results of coverability, which include recursive vector addition system with states [1], multi-set pushdown systems [2, 3], and a WSPDS with finite control states and well-quasi-ordered stack alphabet.リサーチレポート（北陸先端科学技術大学院大学情報科学研究科