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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25112 |
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Table of 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.