Towards an Efficient Tree Automata based technique for Timed Systems

TL;DR

This paper introduces an efficient tree automata-based method for analyzing recursive real-time systems, providing theoretical improvements and a prototype tool for practical implementation.

Contribution

It develops a novel approach combining graph modeling and tree automata to analyze timed systems with recursion, achieving optimal complexity and practical efficiency.

Findings

Bound on tree-width of system behaviors enables automata construction

Finite tree automaton emptiness checks system realizability

Prototype tool demonstrates practical analysis of timed recursive systems

Abstract

The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique consists of modeling the behaviours of the timed system as graphs, and interpreting these graphs on tree terms by showing a bound on their tree-width. We then build a tree automaton that accepts exactly those tree terms that describe realizable runs of the timed system. The emptiness of the timed system thus boils down to emptiness of a finite tree automaton that accepts these tree terms. This approach helps us in obtaining an optimal complexity, not just in theory (as done in earlier work), but also in going towards an efficient implementation of our technique. To do this, we make several improvements in the theory and exploit these to build a first prototype tool that can analyze timed systems with recursion.