Abstract Model Repair

TL;DR

This paper introduces an abstraction refinement framework for model repair in Kripke structures using 3-valued CTL semantics, effectively addressing state explosion issues in large or infinite models.

Contribution

It proposes a novel abstract-model-repair algorithm with proven soundness and semi-completeness, and demonstrates its practical utility through prototype implementation.

Findings

Effective handling of large state spaces via abstraction refinement

Successful repair of models in practical case studies

Algorithm proven to be sound and semi-complete

Abstract

Given a Kripke structure M and CTL formula $\varphi$, where M does not satisfy $\varphi$, the problem of Model Repair is to obtain a new model M' such that M' satisfies $\varphi$. Moreover, the changes made to M to derive M' should be minimum with respect to all such M'. As in model checking, state explosion can make it virtually impossible to carry out model repair on models with infinite or even large state spaces. In this paper, we present a framework for model repair that uses abstraction refinement to tackle state explosion. Our framework aims to repair Kripke Structure models based on a Kripke Modal Transition System abstraction and a 3-valued semantics for CTL. We introduce an abstract-model-repair algorithm for which we prove soundness and semi-completeness, and we study its complexity class. Moreover, a prototype implementation is presented to illustrate the practical utility of abstract-model-repair on an Automatic Door Opener system model and a model of the Andrew File System 1 protocol.