Extended Computation Tree Logic

Abstract

Abstract. We introduce a generic extension of the popular branchingtime logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property may be fulfilled. We consider several classes of languages leading to logics with different expressive power and complexity, whose importance is motivated by their use in model checking, synthesis, abstract interpretation, etc. We show that even with context-free languages on the until operator the logic still allows for polynomial time model-checking despite the significant increase in expressive power. This makes the logic a promising candidate for applications in verification. In addition, we analyse the complexity of satisfiability and compare the expressive power of these logics to CTL * and extensions of PDL.

Ockhamist Propositional Dynamic Logic: A Natural Link between PDL and CTL*

“…While the branching-time temporal logic CTL * is compatible with the Ockhamist conception of time, the semantics for PDL in terms of labelled transition systems is closer to the Peircean view than to the Ockhamist view since it does not consider a notion of actual history or actual path in a transition system. The logic OPDL can be conceived as a variant of the logic of programs PDL based on the 1 It is worth noting that Axelsson et al [2] have recently studied generic extensions of CTL in which temporal operators are parameterized with different kinds of formal languages recognized by different classes of automata (e.g., regular languages, visibly pushdown and contextfree languages). They compare the expressive power of these extensions of PDL to CTL, PDL and extensions of PDL such as PDL-∆.…”

“…They compare the expressive power of these extensions of PDL to CTL, PDL and extensions of PDL such as PDL-∆. However, they also show that CTL * cannot be embedded in any of these extensions of CTL, as the property of fairness is expressible in CTL * but is not expressible is any of these logics (see [2,Theorem 4.3]).…”

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

“…a n−1 , s n for some n ∈ N such that s i Let L be a class of languages. We define the logic PDL 0 [L] in negation normal form using a CTL-like syntax [2]-that is, EF L ϕ stands for the PDL-expression L ϕ for instance. The formulas are given by the grammar…”

“…The main difficulty should be the incorporation of Theorem 3 into transition systems. The considered logic is exactly the EF-/AG-fragment of the Extended Computation Tree Logic [2], say CTL[L]. This observation poses at least two questions.…”

“…[CFL] = ∆PDL ? [DCFL] in [2]. languages [1], VPL, the class of deterministic context-free languages, DCFL, and context-free languages, CFL.…”