Computation Tree Logic for Synchronization Properties

TL;DR

This paper introduces a syntactic extension of CTL that can express complex synchronization properties, remains decidable, and has a model-checking complexity in Delta_3^P, enabling analysis of non-regular properties.

Contribution

It proposes a new variant of CTL with reordered quantifiers to express synchronization properties, maintaining decidability and manageable complexity.

Findings

The new logic can express non-regular properties.

Model-checking remains in Delta_3^P complexity class.

Classical bisimulation applies for state-space reduction.

Abstract

We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the same path quantifiers and temporal operators as in CTL, but allowing a different order of the quantifiers. This small syntactic variation induces a logic that can express non-regular properties for which known extensions of MSO with equality of path length are undecidable. We show that our variant of CTL is decidable and that the model-checking problem is in Delta_3^P = P^{NP^NP}, and is DP-hard. We analogously consider quantifier exchange in extensions of CTL, and we present operators defined using basic operators of CTL* that express the occurrence of infinitely many synchronization points. We show that the model-checking problem remains in Delta_3^P. The distinguishing power of CTL and of our new logic coincide if the Next operator is allowed in the logics, thus the classical bisimulation quotient can be used for state-space reduction before model checking.