Bounded Validity Checking of Interval Duration Logic

A rich dense-time logic called Interval Duration Logic(IDL) is useful for specifying quantitative properties of timed systems. The logic is undecidable in general. However, several approaches can be used for checking validity (and model checking) of IDL formulae in practice. In this paper, we propose bounded validity checking of IDL formulae by polynomially reducing this to finding un-satisfying assignment of linsat formulae. We implement this technique and give some performance results obtained by solving the resulting lin-sat formulae using the ICS solver. We also experimentally compare several approaches for checking validity of IDL formulae including (a) digitization followed by automata theoretic analysis, (b) digitization followed by pure propositional SAT solving, and (c) lin-sat solving as proposed in this paper. The comparison uses a rich set of examples drawn from the Duration Calculus literature.