The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks

Di Zhang

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arXiv · 2510.25112

The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks

Di Zhang

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Abstract

This paper introduces a novel paradigm for the analysis and verification of concurrent programs -- the Singularity Theory. We model the execution space of a concurrent program as a branched topological space, where program states are points and state transitions are paths. Within this framework, we characterize deadlocks as attractors and livelocks as non-contractible loops in the execution space. By employing tools from algebraic topology, particularly homotopy and homology groups, we define a series of concurrent topological invariants to systematically detect and classify these concurrent "singularities" without exhaustively traversing all states. This work aims to establish a geometric and topological foundation for concurrent program verification, transcending the limitations of traditional model checking.

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Di Zhang. 2025-10-29. The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks. https://arxiv.org/abs/2510.25112

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