A complete axiomatisation for timed automata

Abstract

In this paper we present a complete proof system for timed automata. It extends our previous axiomatisation of timed bisimulation for the class of loop-free timed automata with unique fixpoint induction. To our knowledge, this is the first algebraic theory for the whole class of timed automata with a completeness result, thus fills a gap in the theory of timed automata. The proof of the completeness result relies on the notion of symbolic timed bisimulation, adapted from the work on value–passing processes.