An extended and more practical mwp flow analysis

TL;DR

This paper presents an improved, more practical method for analyzing imperative programs to certify polynomial bounds on value sizes, incorporating non-determinism management, modularity, and efficiency considerations.

Contribution

It introduces a refined analysis technique that handles non-determinism, extends to function calls, and improves modularity and efficiency in resource-bound certification.

Findings

Enhanced analysis handles non-determinism effectively

Supports modular analysis with function calls

Improves efficiency of matrix operations in analysis

Abstract

We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and offers an innovative way of completing the analysis when a non-polynomial growth is found. We furthermore enrich the analyzed language by adding function definitions and calls, allowing to compose the analysis of different libraries and offering generally more modularity. The implementation of our improved method, discussed in a tool paper (https://hal.archives-ouvertes.fr/hal-03269121), also required to reason about the efficiency of some of the needed operations on the matrices produced by the analysis. It is our hope that this work will enable and facilitate static analysis of source code to guarantee its correctness with respect to resource usages.