Deducing fairness properties in UNITY logic—a new completeness result

Abstract

We explore the use of UNITY logic in specifying and verifying fairness properties of UNITY and UNITY-like programs whose semantics can be modeled by weakly fair transition systems. For such programs, strong fairness properties in the form of “if p holds infinitely often then q also holds infinitely often □◊p⇒□◊q, can be expressed as conditional UNITY properties of the form of “Hypothesis: true→p Conclusion:true→q”. We show that UNITY logic is relatively complete for proving such properties; in the process, a simple inference rule is derived. Specification and verification of weak fairness properties are also discussed.