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Bisimilarity is not Borel†

Published online by Cambridge University Press:  09 December 2015

PEDRO SÁNCHEZ TERRAF
PEDRO SÁNCHEZ TERRAF*
Affiliation:
CIEM-FAMAF, Universidad Nacional de Córdoba, Medina Allende s/n (Ciudad Universitaria), X5000HUA – Córdoba, Argentina Email: sterraf@famaf.unc.edu.ar Algebraische und Logische Grundlagen der Informatik – Institut für Theoretische Informatik – Technische Universität Dresden – Fakultät Informatik – 01062 Dresden
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Abstract

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We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ11-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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 7: Special Issue: Coalgebraic Logic , October 2017 , pp. 1265 - 1284
Copyright
Copyright © Cambridge University Press 2015 

Footnotes

†

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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