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The Termination/Boundedness Problem of Well-Structured Pushdown Systems

Recently, models that combine vector addition systems and pushdown systems have attracted lots of attentions. They can model some classes of concurrent recursive computations, still enjoying certain decidability properties. A well-structured pushdown system (WSPDS) [1] has been proposed to unify such models. It extends a pushdown system with (possibly infinitely many) well-quasi-ordered states and stack alphabet. Several properties, such as coverability, termination, and boundedness, were shown to be decidable under restrictions of either a finite set of states or finite stack alphabet. Inspired by the work [2] of Leroux et. al., this paper shows that the termination and boundedness problems of a general WSPDS are decidable, and gives the lower and upper bounds for a subclass of WSPDS, which are both Hyper-Ackermannian. Compared with [2], our generalization considers well-quasi-ordered stack alphabet rather than finite stack alphabet, whereas [2] considers a WSPDS with finite stack alphabet (but with well-quasi-ordered states).