Structural Abstraction and Selective Refinement for Formal Verification

TL;DR

This paper introduces a novel structural abstraction method for formal verification of robot environments, significantly improving efficiency by selective refinement and enabling practical verification of complex scenarios.

Contribution

The paper proposes a new structural abstraction approach for robot environment modeling and an automated verification workflow inspired by CEGAR, enhancing model-checking efficiency.

Findings

Counterexamples found in minutes for high-resolution scenarios

Direct model-checking crashed after days on the same scenarios

Automated workflow is feasible and effective for complex environments

Abstract

Safety verification of robot applications is extremely challenging due to the complexity of the environment that a robot typically operates in. Formal verification with model-checking provides guarantees but it may often take too long or even fail for complex models of the environment. A usual solution approach is abstraction, more precisely behavioral abstraction. Our new approach introduces structural abstraction instead, which we investigated in the context of voxel representation of the robot environment. This kind of abstraction leads to abstract voxels. We also propose a complete and automated verification workflow, which is based on an already existing methodology for robot applications, and inspired by the key ideas behind counterexample-guided abstraction refinement (CEGAR) - performing an initial abstraction and successively introducing refinements based on counterexamples, intertwined with model-checker runs. Hence, our approach uses selective refinement of structural abstractions to improve the runtime efficiency of model-checking. A fully-automated implementation of our approach showed its feasibility, since counterexamples have been found for a realistic scenario with a fairly high (maximal) resolution in a few minutes, while direct model-checker runs led to a crash after a couple of days.