Well - structured pushdown system , Part 1 : Decidable classes for coverability ?

Pushdown systems (PDSs) model single-thread recursive programs, and well-structured transition systems (WSTSs), such as vector addition systems, are useful to represent non-recursive multi-thread programs. Combining these two ideas, our goal is to investigate wellstructured pushdown systems (WSPDSs), pushdown systems with wellquasi-ordered control states and stack alphabet. This paper focuses on subclasses of WSPDSs, in which the coverability becomes decidable. We apply WSTS-like techniques on classical Pautomata. 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. As examples, we show that the coverability is decidable for recursive vector addition system with states, multi-set pushdown systems, and a WSPDS with finite control states and well-quasi-ordered stack alphabet.