Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
158 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Bisimilarity is not Borel (1211.0967v3)

Published 5 Nov 2012 in math.LO and cs.LO

Abstract: We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_11$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and nondeterministic 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.

Citations (3)

Summary

We haven't generated a summary for this paper yet.