Branching vs. Linear Time: Final Showdown

Abstract. The discussion of the relative merits of linear- versus branching-time frameworks goes back to early 1980s. One of the beliefs dominating this discussion has been that “while specifying is easier in LTL (linear-temporal logic), verification is easier for CTL (branching-temporal logic)”. Indeed, the restricted syntax of CTL limits its expressive power and many important behaviors (e.g., strong fairness) can not be specified in CTL. On the other hand, while model checking for CTL can be done in time that is linear in the size of the specification, it takes time that is exponential in the specification for LTL. Because of these arguments, and for historical reasons, the dominant temporal specification language in industrial use is CTL. In this paper we argue that in spite of the phenomenal success of CTL-based model checking, CTL suffers from several fundamental limitations as a specification language, all stemming from the fact that CTL is a branching-time formalism: the language is unintuitive and hard to use, it does not lend itself to compositional reasoning, and it is fundamentally incompatible with semi-formal verification. These inherent limitations severely impede the functionality of CTL-based model checkers. In contrast, the linear-time framework is expressive and intuitive, supports compositional reasoning and semi-formal verification, and is amenable to combining enumerative and symbolic search methods. While we argue in favor of the linear-time framework, we also we argue that LTL is not expressive enough, and discuss what would be the “ultimate ” temporal specification language.