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Abstract. We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa). We contribute to show that scoped Mpa are indeed a robust model of computation, by focusing on the corresponding theory of visibly Mpa (Mvpa). We prove the equivalence of the deterministic and nondeterministic versions and show that scopebounded computations of an n-stack Mvpa can be simulated, rearranging the input word, by using only one stack. These results have several interesting consequences, such as, the closure under complement, the decidability 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.

Temporal logics for nested words are a specification formalism for procedural programs, since they express requirements about matching calls and returns. We extend this formalism to multiply nested words, which are natural models of the computations of concurrent programs. We study both the satisfiability and the model-checking problems, when the multiply nested words are runs of multi-stack pushdown systems (Mpds). In particular, through a tableau-based construction, we define a Büchi Mpds for the models of a given formula. As expected both problems are undecidable, thus we consider some meaningful restrictions on the Mpds, and show decidability for the considered problems.

Abstract. We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa). We contribute to show that scoped Mpa are indeed a robust model of computation, by focusing on the corresponding theory of visibly Mpa (Mvpa). We prove the equivalence of the deterministic and nondeterministic versions and show that scopebounded computations of an n-stack Mvpa can be simulated, rearranging the input word, by using only one stack. These results have several interesting consequences, such as, the closure under complement, the decidability 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.