# Semantic minimizations for temporal logics

## Michael Huth

(Imperial College London)

Three-valued models, in which properties of a system are either true,

false or unknown, have recently been advocated as a better

representation for reactive program abstractions generated by automatic

techniques such as predicate abstraction. Indeed, for the same cost,

model checking three-valued abstractions can be used to both prove and

disprove any temporal-logic property, whereas traditional conservative

abstractions can only prove universal properties. Also, verification

results can be more precise with generalized model checking, which

checks whether there exists a concretization of an abstraction

satisfying a temporal-logic formula. Since generalized model checking

includes satisfiability as a special case (when everything in the model

is unknown), it is in general more expensive than traditional model

checking. In this talk, we study how to reduce generalized model

checking to model checking by a temporal-logic formula transformation,

which generalizes a transformation for propositional logic known as

semantic minimization in the literature. We show that many

temporal-logic formulas of practical interest are self-minimizing, i.e.,

are their own semantic minimizations, and hence that model checking for

these formulas has the same precision as generalized model checking.

(Joint work with Patrice Godefroid.)

**Thursday 2nd March 2006, 14:00**

Robert Recorde Room

Department of Computer Science