Are Timed Automata Bad for a Specification Language? Language Inclusion Checking for Timed Automata

Ting Wang, Jun Sun, Yang Liu, Xinyu Wang, Shanping Li

Abstract: Given a timed automaton $\cal P$ modeling an implementation and a timed automaton $\cal S$ as a specification, language inclusion checking is to decide whether the language of $\cal P$ is a subset of that of $\cal S$ . It is known that this problem is undecidable and “this result is an obstacle in using timed automata as a specification language” [2]. This undecidability result, however, does not imply that all timed automata are bad for specification. In this work, we propose a zone-based semi-algorithm for language inclusion checking, which implements simulation reduction based on Anti-Chain and LU-simulation. Though it is not guaranteed to terminate, we show that it does in many cases through both theoretical and empirical analysis. The semi-algorithm has been incorporated into the PAT model checker, and applied to multiple systems to show its usefulness and scalability.