Sublogics of a branching time logic of robustness

Abstract

In this paper we study sublogics of RoCTL*, a recently proposed logic for specifying robustness. RoCTL* allows specifying robustness in terms of properties that are robust to a certain number of failures. RoCTL* is an extension of the branching time logic CTL* which in turn extends CTL by removing the requirement that temporal operators be paired with path quantifiers. In this paper we consider three sublogics of RoCTL*. We present a tableau for RoBCTL*, a bundled variant of RoCTL* that allows fairness constraints to be placed on allowable paths. We then examine two CTL-like restrictions of CTL*. Pair-RoCTL* requires a temporal operator to be paired with a path quantifier; we show that Pair-RoCTL* is as hard to reason about as the full CTL*. State-RoCTL* is restricted to State formulas, and we show that there is a linear truth preserving translation of State-RoCTL into CTL, allowing State-RoCTL to be reasoned about as efficiently as CTL.