A multi-stack pushdown system is a natural model of concurrent programs. The basic verification problems are undecidable and a common trend is to consider under-approximations of the system behaviors to gain decidability. In this paper, we restrict the semantics such that a symbol that is pushed onto a stack s can be popped only within a given number of contexts involving s, i.e., we bound the scope (in terms of number of contexts) of matching push and pop transitions. This restriction permits runs with unboundedly many contexts even between matching push and pop transitions (for systems with at least three stacks). We call the resulting model a multi-stack pushdown system with scope-bounded matching relations (SMpds). We show that the configuration reachability and the location reachability problems for SMpds are both Pspace-complete, and that the set of the reachable configurations can be captured by a finite automaton.

多堆栈下推系统是并发程序的自然模型。基本的验证问题是无法确定的，一个普遍的趋势是考虑系统行为的近似值以获得可确定性。在本文中，我们对语义进行了限制，以使被压入堆栈s的符号只能在涉及s的给定数量的上下文中弹出，即，我们限制了匹配push和的范围（根据上下文的数量）弹出过渡。此限制甚至允许在匹配的推式和弹出式转换之间（对于具有至少三个堆栈的系统）在无数个上下文的情况下运行。我们将结果模型称为具有范围边界匹配关系的多堆栈下推系统（SMpds）。我们表明，SMpds的配置可及性和位置可及性问题都是Pspace完全的，并且可配置的集合可以由有限自动机捕获。