Model and program repair via SAT solving

Abstract

We consider the following model repair problem: given a finite Kripke structure M and a specification formula η in some modal or temporal logic, determine if M contains a substructure M ′ (with the same initial state) that satisfies η. Thus, M can be "repaired" to satisfy the specification η by deleting some transitions.We map an instance (M, η) of model repair to a boolean formula repair (M, η) such that (M, η) has a solution iff repair (M, η) is satisfiable. Furthermore, a satisfying assignment determines which transitions must be removed from M to generate a model M ′ of η. Thus, we can use any SAT solver to repair Kripke structures. Furthermore, using a complete SAT solver yields a complete algorithm: it always finds a repair if one exists.We extend our method to repair finite-state shared memory concurrent programs, to solve the discrete event supervisory control problem [18,19], to check for the existence of symmettric solutions [12], and to accomodate any boolean constraint on the existence of states and transitions in the repaired model.Finally, we show that model repair is NP-complete for CTL, and logics with polynomial model checking algorithms to which CTL can be reduced in polynomial time. A notable example of such a logic is Alternating-Time Temporal Logic (ATL).