From Discrete Duration Calculus to Symbolic Automata

The goal of this paper is to translate (fragments of) the quantified discrete duration calculus QDDC, proposed by P. Pandya, into symbolic acceptors with counters. Acceptors are written in the synchronous programming language Lustre, in order to allow available symbolic verification tools (model-checkers, abstract interpreters) to be applied to properties expressed in QDDC. We show that important constructs of QDDC need non-deterministic acceptors, in order to be translated with a bounded number of counters, and an expressive fragment of the logic is identified and translated. Then, we consider a more restricted fragment, which only needs deterministic acceptors.