On Timed Scope-Bounded Context-Sensitive Languages

Abstract

In (DLT 2016) we studied timed context sensitive languages characterized by multiple stack push down automata (MPA), with an explicit bound on number of stages where in each stage at most one stack is used (k-round MPA). In this paper, we continue our work on timed MPA and study a subclass in which a symbol corresponding to a stack being pushed in it must be popped within fixed number of contexts of that stack -scope-bounded push-down automata with multiple stacks (k-scope MPA). We use Visibly Push-down Alphabet and Event Clocks to show that timed k-scope MPA have decidable reachability problem; are closed under Boolean operations; and have an equivalent logical characterization.

Reachability relations of timed pushdown automata

“…Subsequent works building on dtpda include nested timed automata (stack of ta which can be pushed and popped), whose nonemptiness problem reduce to dtpda [54], input/output dtpda [55,56], visible dtpda [12], and classes of decidable timed multistack languages closed under Boolean operations (i.e., a so called perfect class), such as round-bounded [13], later generalised to scopebounded [14]. Alternative analyses of the elegant dtpda construction have been performed, e.g., via a subclass of pushdown automata with stack manipulation [67] and well-structured pushdown systems [18].…”

Scope-Bounded Reachability in Valence Systems

“…Furthermore, after their introduction [25] scope-bounded multi-pushdown systems have been studied in terms of accepted languages [26], temporal logic model checking [28,3]. Moreover, scope-boundedness has been studied in the timed setting [2], [4].…”