Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25112 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918177675411456 |
|---|---|
| author | Zhang, Di |
| author_facet | Zhang, Di |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks Zhang, Di Programming Languages Distributed, Parallel, and Cluster Computing Logic in Computer Science Algebraic Topology 68Q85, 55P99, 68N30, 55U10 D.2.4; F.3.1; D.1.3; F.1.2 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. |
| title | The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks |
| topic | Programming Languages Distributed, Parallel, and Cluster Computing Logic in Computer Science Algebraic Topology 68Q85, 55P99, 68N30, 55U10 D.2.4; F.3.1; D.1.3; F.1.2 |
| url | https://arxiv.org/abs/2510.25112 |