Applications of Polyhedral Computations to the Analysis and Verification of Hardware and Software Systems

TL;DR

This paper surveys how convex polyhedra are used in static analysis and verification of systems, discussing different classes, operations, and combinations with other abstractions to improve analysis precision.

Contribution

It provides a comprehensive overview of polyhedral computations in system analysis, highlighting potential for theoretical advances and practical applications.

Findings

Various classes of polyhedra are used in analysis.

Polyhedral operations are essential for verification tasks.

Combining polyhedra with other abstractions can enhance precision.

Abstract

Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate complexity-precision trade-off is a particularly acute problem, so that the availability of a wide spectrum of alternative solutions is mandatory. We survey the range of applications of polyhedral computations in this area; give an overview of the different classes of polyhedra that may be adopted; outline the main polyhedral operations required by automatic analyzers and verifiers; and look at some possible combinations of polyhedra with other numerical abstractions that have the potential to improve the precision of the analysis. Areas where further theoretical investigations can result in important contributions are highlighted.