Reducing CTL-live model checking to semantic entailment in first-order logic (version 1)

Abstract

The core of temporal logic model checking is the reachability problem, which is not expressible in first-order logic (FOL). Most model checking algorithms, both for finite and infinite Kripke structures, contain a loop that iterates to reach a fixed-point. As a result, reasoners with input languages no more expressive than FOL have been used iteratively for model checking rather than having the reasoner solve the problem completely by itself. In this article, we present a method for reducing model checking of finite and infinite Kripke structures that are expressed in FOL to entailment checking in FOL for a fragment of computational tree logic (CTL), which we call CTL-live. CTL-live includes all the CTL connectives that are expressible in the mu-calculus using the least fixed-point operator. These connectives are traditionally used to express liveness properties. This reduction allows us to consider model checking of CTL-live as a FOL theorem proving problem, and to use directly FOL reasoning techniques for model checking without the need of fixed-point operators, transitive-closure, or induction. We prove that CTL-live is maximal in the sense that model checking of CTL connectives that are not included in CTL-live is not reducible to semantic entailment in FOL.