{"ID":2848341,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25112","arxiv_id":"2510.25112","title":"The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks","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.","short_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 deadloc...","url_abs":"https://arxiv.org/abs/2510.25112","url_pdf":"https://arxiv.org/pdf/2510.25112v1","authors":"[\"Di Zhang\"]","published":"2025-10-29T02:24:07Z","proceeding":"cs.PL","tasks":"[\"cs.PL\",\"cs.DC\",\"cs.LO\",\"math.AT\"]","methods":"[]","has_code":false}