Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison
Model checking is a powerful method widely explored in formal verification to check the (state-transition) model of a system against desired properties of its behaviour. Classically, properties are expressed by formulas of a temporal logic, such as LTL, CTL, and CTL*. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. On the contrary, Halpern and Shoham's interval temporal logic (HS) is "interval-wise" interpreted, thus allowing one to naturally
... one to naturally express properties of computation stretches, spanning a sequence of states, or properties involving temporal aggregations, which are inherently "interval-based". In this paper, we study the expressiveness of HS in model checking, in comparison with that of the standard logics LTL, CTL, and CTL*. To this end, we consider HS endowed with three semantic variants: the state-based semantics, introduced by Montanari et al., which allows branching in the past and in the future, the linear-past semantics, allowing branching only in the future, and the linear semantics, disallowing branching. These variants are compared, as for their expressiveness, among themselves and to standard temporal logics, getting a complete picture. In particular, HS with linear (resp., linear-past) semantics is proved to be equivalent to LTL (resp., finitary CTL*). 1 Introduction Point-based temporal logics (PTLs) provide a fundamental framework for the specification of the behavior of reactive systems, that makes it possible to describe how the system evolves state-by-state ("point-wise" view). PTLs have been successfully employed in model checking (MC), which enables one to automatically verify complex finite-state systems usually modelled as finite propositional Kripke structures. The MC methodology considers two types of PTLs-linear and branching-which differ in the underlying model of time. In linear temporal logics, such as LTL , each moment in time has a unique possible future: formulas are interpreted over paths of a Kripke structure, and thus they refer to a single computation of the system. In branching temporal logics, such as CTL and CTL * , each moment in time may evolve into several possible futures: formulas are interpreted over states of the Kripke structure, hence referring to all the possible computations of a system.