Murano / Branching - Time Temporal Logics with Minimal Model Quantifiers

Temporal logics are a well investigated formalism for the specification and verification of 6 reactive systems. Using formal verification techniques, one can ensure the correctness of a system 7 with respect to a desired behavior, i.e., the specification, by verifying whether a model of the former 8 satisfies a temporal logic formula expressing the latter. In this setting, a very crucial aspect is to 9 reasoning about substructures of the entire model. Indeed, for several fundamental problems, the 10 formal verification approach requires to select a portion of the model of interest on which to verify a 11 specific property. 12 In this paper, we introduce a new logic framework that allows to select automatically desired parts of 13 the system to be successively verified. Specifically, we extend the classical branching-time temporal 14 logic CTL∗ by means of minimal model operators (MCTL∗, for short). These operators allow to 15 extract, from a model, minimal submodels on which we can check a specification, which is also given 16 by an MCTL∗ formula. We interpret the logic under three different semantics, called minimal (m), 17 minimal-unwinding (mu), and unwinding-minimal (um), which differ one from another on the way a 18 substructure is extracted and then checked in the verification process. We show that both MCTLm 19 and MCTLmu are strictly more expressive than CTL∗, since these logics are sensible to unwinding 20 and not invariant under bisimulation. Conversely, MCTLum preserves both these properties. As 21 far as the satisfiability concerns, we prove that MCTLm and MCTLmu are highly undecidable. 22 We further investigate some syntactic fragments of MCTL∗, such as MCTL, for which we obtain 23 interesting results. 24