To be fair, use bundles

Abstract

Attempts to manage the reasoning about systems with fairness properties are long running. The popular but restricted Computational Tree Logic (CTL) is amenable to automated reasoning but has difficulty expressing some fairness properties. More expressive languages such as CTL* and CTL+ are computationally complex. The main contribution of this paper is to show the usefulness and practicality of employing the bundled variants of these languages to handle fairness. In particular we present a tableau for a bundled variant of CTL that still has the similar computational complexity to the CTL tableau and a simpler implementation. We further show that the decision problem remains in EXPTIME even if a bounded number of CTL* fairness constraints are allowed in the input formulas. By abandoning limit closure the bundled logics can simultaneously be easier to automate and express many typical fairness constraints.