Language Inclusion Checking of Timed Automata with Non-Zenoness

Given a timed automaton P modeling an implementation and a timed automaton S as a specification, the problem of language inclusion checking is to decide whether the language of P is a subset of that of S. It is known to be undecidable. The problem gets more complicated if non-Zenoness is taken into consideration. A run is Zeno if it permits infinitely many actions within finite time. Otherwise it is non-Zeno. Zeno runs might present in both P and S. It is necessary to check whether a run is Zeno or not so as to avoid presenting Zeno runs as counterexamples of language inclusion checking. In this work, we propose a zone-based semi-algorithm for language inclusion checking with non-Zenoness. It is further improved with simulation reduction based on LU-simulation. Though our approach is not guaranteed to terminate, we show that it does in many cases through empirical study. Our approach has been incorporated into the PAT model checker, and applied to multiple systems to show its usefulness.