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Bisimilarity is not Borel


We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it.

This has an impact on the theory of probabilistic and non-deterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.

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Partially supported by CONICET, ANPCyT project PICT 2012-1823, SeCyT-UNC project 05/B284, and EU 7FP grant agreement 295261 (MEALS). Part of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logics.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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