A MONA-based Decision Procedure for Propositional Interval Temporal Logic

Interval Temporal Logic (ITL) is a finite-time linear temporal logic with applications in hardware verifi-

cation, temporal logic programming and specification of multimedia documents. Due to the inherently non-

elementary complexity of its decision problem, efficient ITL-based verification tools have been difficult to de-

velop. We give a new decision procedure for Propositional ITL (PITL) implemented on top of MONA, an

efficient automata-based decision procedure for the logic WS1S. Despite the non-elementary complexity of

WS1S, MONA has been successfully applied in problems such as hardware synthesis, protocol verification and

theorem proving. We have developed a new semantics for PITL based on WS1S formulas, which led us to an

easy translation to MONA programs. We have implemented the translation algorithm in C, and the general

efficiency of the decision procedure is a direct consequence of the many optimisations included in MONA (e.g.

BDDs, DAGification and formula reductions). To our knowledge, this is one of the very few implementations

of a decision procedure for PITL with projection, and the first one based on automata.