A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915144322252800 |
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| author | van Glabbeek, Rob Groote, Jan Friso de Vink, Erik |
| author_facet | van Glabbeek, Rob Groote, Jan Friso de Vink, Erik |
| contents | This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a basic, recursion-free process language with non-deterministic as well as probabilistic choice. The proof of completeness of the axiomatization builds on the completeness of strong probabilistic bisimilarity on the one hand and on the notion of a concrete process, i.e. a process that does not display (partially) inert $τ$-moves, on the other hand. The approach is first presented for the non-deterministic fragment of the calculus and next generalized to incorporate probabilistic choice, too. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_05631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice van Glabbeek, Rob Groote, Jan Friso de Vink, Erik Logic in Computer Science F.3.1 This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a basic, recursion-free process language with non-deterministic as well as probabilistic choice. The proof of completeness of the axiomatization builds on the completeness of strong probabilistic bisimilarity on the one hand and on the notion of a concrete process, i.e. a process that does not display (partially) inert $τ$-moves, on the other hand. The approach is first presented for the non-deterministic fragment of the calculus and next generalized to incorporate probabilistic choice, too. |
| title | A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice |
| topic | Logic in Computer Science F.3.1 |
| url | https://arxiv.org/abs/2502.05631 |