Analyzing Timed Systems Using Tree Automata

TL;DR

This paper introduces a novel method for analyzing timed systems by translating their behaviors into graphs with bounded tree-width and using tree automata to verify properties, offering a general approach beyond traditional automata.

Contribution

The paper presents a new technique that employs finite tree automata to analyze timed systems via graph representations, extending analysis capabilities to systems like timed pushdown automata.

Findings

Applicable to timed pushdown systems and automata

Enables checking MSO-definable properties of timed behaviors

Provides a general framework for timed system analysis

Abstract

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions).