Ergodic properties of concurrent systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910952992014336 |
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| author | Abbes, Samy Jugé, Vincent |
| author_facet | Abbes, Samy Jugé, Vincent |
| contents | A concurrent system is defined as a monoid action of a trace monoid on a finite set of states. Concurrent systems represent state models where the state is distributed and where state changes are local. Starting from a spectral property on the combinatorics of concurrent systems, we prove the existence and uniqueness of a Markov measure on the space of infinite trajectories relatively to any weight distributions. In turn, we obtain a combinatorial result by proving that the kernel of the associated Möbius matrix has dimension 1; the Möbius matrix extends in this context the Möbius polynomial of a trace monoid. We study ergodic properties of irreducible concurrent systems and we prove a Strong law of large numbers. It allows us to introduce the speedup as a measurement of the average amount of concurrency within infinite trajectories. Examples are studied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_12810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic properties of concurrent systems Abbes, Samy Jugé, Vincent Probability Discrete Mathematics Group Theory A concurrent system is defined as a monoid action of a trace monoid on a finite set of states. Concurrent systems represent state models where the state is distributed and where state changes are local. Starting from a spectral property on the combinatorics of concurrent systems, we prove the existence and uniqueness of a Markov measure on the space of infinite trajectories relatively to any weight distributions. In turn, we obtain a combinatorial result by proving that the kernel of the associated Möbius matrix has dimension 1; the Möbius matrix extends in this context the Möbius polynomial of a trace monoid. We study ergodic properties of irreducible concurrent systems and we prove a Strong law of large numbers. It allows us to introduce the speedup as a measurement of the average amount of concurrency within infinite trajectories. Examples are studied. |
| title | Ergodic properties of concurrent systems |
| topic | Probability Discrete Mathematics Group Theory |
| url | https://arxiv.org/abs/2505.12810 |