On Solving Temporal Logic Queries

Temporal query checking is an extension of temporal model checking where one asks what propositional formulae can be inserted in a temporal query (a temporal formula with a placeholder) so that the resulting formula is satisfied in the model at hand. We study the problem of computing all minimal solutions to a temporal query without restricting to so-called “valid” queries (queries guaranteed to have a unique minimal solution). While this problem is intractable in general, we show that deciding uniqueness of the minimal solution (and computing it) can be done in polynomial-time.