Trace Spaces: an Efficient New Technique for State-Space Reduction

TL;DR

This paper introduces a novel algebraic topology-based algorithm for state-space reduction in concurrent program analysis, significantly improving efficiency over existing partial-order reduction methods.

Contribution

It presents a new geometric semantics framework and an algorithm to compute dihomotopy classes, enabling more efficient state-space reduction in model checking.

Findings

Preliminary implementation shows promising efficiency gains.

Algorithm effectively computes reduced control-flow graphs with loops.

Results outperform traditional partial-order reduction techniques.

Abstract

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing loops, which is "as reduced as possible" in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques.