(In)finite Trace Equivalence of Probabilistic Transition Systems

We show how finite and infinite trace semantics of generative probabilistic transition systems arises through a determinisation construction. This enables the use of bisimulations (up-to) to prove equivalence. In particular, it follows that trace equivalence for finite probabilistic transition systems is decidable. Further, the determinisation construction applies to both discrete and continuous probabilistic systems.

[1]  Michele Boreale,et al.  Weighted Bisimulation in Linear Algebraic Form , 2009, CONCUR.

[2]  Damien Pous,et al.  Checking NFA equivalence with bisimulations up to congruence , 2013, POPL.

[3]  Corina Cîrstea.  From Branching to Linear Time, Coalgebraically , 2017, Fundam. Informaticae.

[4]  Bart Jacobs,et al.  Introduction to Coalgebra: Towards Mathematics of States and Observation , 2016, Cambridge Tracts in Theoretical Computer Science.

[5]  Ichiro Hasuo,et al.  Coalgebraic Infinite Traces and Kleisli Simulations , 2018, Log. Methods Comput. Sci..

[6]  Barbara König,et al.  Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems , 2013, Log. Methods Comput. Sci..

[7]  A. Sokolova,et al.  Sound and Complete Axiomatization of Trace Semantics for Probabilistic Systems , 2011, MFPS.

[8]  Alexandra Silva,et al.  Generalizing determinization from automata to coalgebras , 2013, Log. Methods Comput. Sci..

[9]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[10]  Alexandre Goy.  Trace semantics via determinization for probabilistic transition systems , 2018, ArXiv.

[11]  Achim Klenke,et al.  Probability theory - a comprehensive course , 2008, Universitext.

[12]  Ana Sokolova,et al.  Probabilistic systems coalgebraically: A survey , 2011, Theor. Comput. Sci..

[13]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[14]  Ana Sokolova,et al.  Generic Trace Semantics via Coinduction , 2007, Log. Methods Comput. Sci..

[15]  Jurriaan Rot,et al.  A general account of coinduction up-to , 2016, Acta Informatica.

[16]  Barbara König,et al.  Up-To Techniques for Weighted Systems , 2017, TACAS.

[17]  Michèle Giry,et al.  A categorical approach to probability theory , 1982 .

[18]  Alexandra Silva,et al.  Trace semantics via determinization , 2015, J. Comput. Syst. Sci..

[19]  Alexandra Silva,et al.  The Power of Convex Algebras , 2017, CONCUR.