# On Timed Scope-bounded Context-sensitive Languages

## TL;DR

This paper introduces a new subclass of timed multi-stack automata called k-scope MPA, which ensures stack symbols are popped within a fixed scope, and demonstrates their decidability, closure properties, and logical characterization.

## Contribution

It defines and analyzes timed k-scope MPA, establishing their decidability, closure under Boolean operations, and providing a logical framework, advancing the understanding of timed context-sensitive languages.

## Key findings

- Decidable reachability problem for timed k-scope MPA
- Closure under Boolean operations
- Logical characterization of the automata

## 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.