mwp-Analysis Improvement and Implementation: Realizing Implicit Computational Complexity

TL;DR

This paper enhances and implements the mwp-flow analysis for implicit computational complexity, making it practical for automatic data-size analysis of C programs and facilitating certified complexity proofs.

Contribution

It fine-tunes and extends the mwp-flow analysis to handle function calls and improves its efficiency for practical use in complexity analysis.

Findings

The analysis is now more tractable and efficient for real-world programs.

It can automatically compute data size bounds for C programs.

The approach enables certified complexity analysis.

Abstract

Implicit Computational Complexity (ICC) drives better understanding of complexity classes, but it also guides the development of resources-aware languages and static source code analyzers. Among the methods developed, the mwp-flow analysis certifies polynomial bounds on the size of the values manipulated by an imperative program. This result is obtained by bounding the transitions between states instead of focusing on states in isolation, as most static analyzers do, and is not concerned with termination or tight bounds on values. Those differences, along with its built-in compositionality, make the mwp-flow analysis a good target for determining how ICC-inspired techniques diverge compared with more traditional static analysis methods. This paper's contributions are threefold: we fine-tune the internal machinery of the original analysis to make it tractable in practice; we extend the analysis to function calls and leverage its machinery to compute the result of the analysis efficiently; and we implement the resulting analysis as a lightweight tool to automatically perform data-size analysis of C programs. This documented effort prepares and enables the development of certified complexity analysis, by transforming a costly analysis into a tractable program, that furthermore decorrelates the problem of deciding if a bound exist with the problem of computing it.