Abstract. We study the formal language theory of multistack push-down automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded num-ber of contexts of S (scoped Mpa). We contribute to show that scoped Mpa are indeed a robust model of computation, by focusing on the cor-responding theory of visibly Mpa (Mvpa). We prove the equivalence of the deterministic and nondeterministic versions and show that scope-bounded computations of an n-stack Mvpa can be simulated, rearrang-ing the input word, by using only one stack. These results have several interesting consequences, such as, the closure under complement, the de-cidability of universality, inclusion and equality, and a Parikh theorem. We also give a logical characterization and compare the expressiveness of the scope-bounded restriction with Mvpa classes from the literature. 1

We give a general approach to show the closure under complement and decide the emptiness for many classes of multistack visibly pushdown automata (Mvpa). A central notion in our approach is the visibly path-tree, i.e., a stack tree with the encoding of a path that denotes a linear ordering of the nodes. We show that the set of all such trees with a bounded size labeling is regular, and path-trees allow us to design simple conversions between tree automata and Mvpa’s. As corollaries of our results we get the closure under complement of ordered Mvpa that was an open problem, and a better upper bound on the algorithm to check the emptiness of bounded-phase Mvpa’s, that also shows that this problem is fixed parameter tractable in the number of phases.

In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a linear-time temporal logic extending well-known logic CaRet but dedicated to multi-pushdown systems in which abstract operators (related to calls and returns) such as those for next-time and until are parameterized by stacks. We show that the problem is EXPTIME-complete for context-bounded runs and unary encoding of the number of context switches; we also prove that the problem is 2EXPTIME-complete for phasebounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input (whence it is not a constant of the model-checking problem), which makes a substantial difference in the complexity. In certain cases, our results improve previous complexity results.

We provide complexity characterizations of model checking multi-pushdown systems. We consider three standard notions for bound-edness: context boundedness, phase boundedness and stack ordering. The logical formalism is a linear-time temporal logic extending well-known operators are parameterized by stacks. We show that the problem is ExpTime-complete for context-bounded runs and unary encoding of the number of context switches; we also prove that the problem is 2ExpTime-complete for phase-bounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input, which makes a substantial difference in the complexity.