Model and Program Repair via SAT Solving

TL;DR

This paper introduces a SAT-based approach for repairing finite Kripke structures and concurrent programs to satisfy modal or temporal logic specifications, providing a complete and adaptable method for model correction.

Contribution

The authors develop a SAT encoding for the model repair problem, extend it to concurrent programs and control problems, and analyze its computational complexity.

Findings

SAT encoding enables effective model repair.

Complete algorithm guarantees finding a repair if it exists.

NP-completeness established for CTL model repair.

Abstract

We consider the following \emph{model repair problem}: given a finite Kripke structure $M$ and a specification formula $\eta$ in some modal or temporal logic, determine if $M$ contains a substructure $M'$ (with the same initial state) that satisfies $\eta$. Thus, $M$ can be ``repaired'' to satisfy the specification $\eta$ by deleting some transitions. We map an instance $(M, \eta)$ of model repair to a boolean formula $\repfor(M,\eta)$ such that $(M, \eta)$ has a solution iff $\repfor(M,\eta)$ is satisfiable. Furthermore, a satisfying assignment determines which transitions must be removed from $M$ to generate a model $M'$ of $\eta$. 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 \cite{RW87,RW89}, to check for the existence of symmettric solutions \cite{ES93}, 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).