Pushdown Timed Automata: a Binary Reachability Characterization and Safety Verification

TL;DR

This paper introduces a decidable characterization of binary reachability for pushdown timed automata using the pattern technique, enabling verification of properties involving dense and unbounded variables.

Contribution

It provides the first decidable characterization of binary reachability for pushdown timed automata, extending verification capabilities beyond classic timed automata.

Findings

Binary reachability of PTAs is decidable using the pattern technique.

Timed automata binary reachability is definable in the additive theory of reals and integers.

Verification of properties with linear relations over dense and discrete variables is now possible.

Abstract

We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL$^*$ for pushdown systems. The results are also extended to other generalizations of timed automata.