Reducing CTL-live model checking to first-order logic validity checking

Abstract

Temporal logic model checking of infinite state systems without the use of iteration or abstraction is usually considered beyond the realm of first-order logic (FOL) reasoners because of the need for a fixpoint computation. In this paper, we show that it is possible to reduce model checking of a finite or infinite Kripke structure that is expressed in FOL to a validity problem in FOL for a fragment of computational tree logic (CTL), which we call CTL-live. CTL-live includes the CTL connectives that are traditionally used to express liveness properties. Our reduction can form the basis for methods that use FOL reasoning techniques directly to accomplish model checking of CTL-live properties without the need for fixpoint operators, transitive closure, abstraction, or induction.