Using non-convex approximations for efficient analysis of timed automata

TL;DR

This paper introduces a novel approach to analyze timed automata by avoiding convex zone extrapolations, enabling more flexible and potentially more efficient reachability analysis with on-the-fly parameter calculation.

Contribution

It proposes a non-convex zone approximation method for timed automata reachability, improving flexibility and efficiency over traditional convex extrapolation techniques.

Findings

Algorithm effectively checks zone inclusion in region closure

On-the-fly parameter calculation improves exploration efficiency

Experimental results show promising performance improvements

Abstract

The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite. In order to make the graph finite, zones are approximated using an extrapolation operator. For reasons of efficiency in current algorithms extrapolation of a zone is always a zone and in particular it is convex. In this paper, we propose to solve the reachability problem without such extrapolation operators. To ensure termination, we provide an efficient algorithm to check if a zone is included in the so called region closure of another. Although theoretically better, closure cannot be used in the standard algorithm since a closure of a zone may not be convex. An additional benefit of the proposed approach is that it permits to calculate approximating parameters on-the-fly during exploration of the zone graph, as opposed to the current methods which do it by a static analysis of the automaton prior to the exploration. This allows for further improvements in the algorithm. Promising experimental results are presented.