A Testing Scenario for Probabilistic Processes

L. Cheung, Mariëlle Ida Antoinette Stoelinga, F.W. Vaandrager

Research output: Book/ReportReportProfessional

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Abstract

We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the well-known trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite probabilistic automata and prove that our notion of observational equivalence coincides with the trace distribution equivalence proposed by Segala. Along the way, we give an explicit characterization of the set of probabilistic executions of an arbitrary probabilistic automaton A and generalize the Approximation Induction Principle by defining an algebraic CPO structure on the set of trace distributions of A. We also prove limit and convex closure properties of trace distributions in an appropriate metric space.
Original languageUndefined
Place of PublicationNijmegen
PublisherRadboud University Nijmegen
Number of pages49
Publication statusPublished - Jan 2006

Publication series

NameICIS
PublisherRadboud University Nijmegen
No.R06002

Keywords

  • CR-F.1.2
  • CR-F.4.3
  • MSC-68Q05
  • MSC-68Q10
  • EWI-6949
  • MSC-68Q75
  • CR-F.1.1
  • METIS-238681
  • IR-66367
  • MSC-68Q55

Cite this

Cheung, L., Stoelinga, M. I. A., & Vaandrager, F. W. (2006). A Testing Scenario for Probabilistic Processes. (ICIS; No. R06002). Nijmegen: Radboud University Nijmegen.
Cheung, L. ; Stoelinga, Mariëlle Ida Antoinette ; Vaandrager, F.W. / A Testing Scenario for Probabilistic Processes. Nijmegen : Radboud University Nijmegen, 2006. 49 p. (ICIS; R06002).
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keywords = "CR-F.1.2, CR-F.4.3, MSC-68Q05, MSC-68Q10, EWI-6949, MSC-68Q75, CR-F.1.1, METIS-238681, IR-66367, MSC-68Q55",
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Cheung, L, Stoelinga, MIA & Vaandrager, FW 2006, A Testing Scenario for Probabilistic Processes. ICIS, no. R06002, Radboud University Nijmegen, Nijmegen.

A Testing Scenario for Probabilistic Processes. / Cheung, L.; Stoelinga, Mariëlle Ida Antoinette; Vaandrager, F.W.

Nijmegen : Radboud University Nijmegen, 2006. 49 p. (ICIS; No. R06002).

Research output: Book/ReportReportProfessional

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N2 - We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the well-known trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite probabilistic automata and prove that our notion of observational equivalence coincides with the trace distribution equivalence proposed by Segala. Along the way, we give an explicit characterization of the set of probabilistic executions of an arbitrary probabilistic automaton A and generalize the Approximation Induction Principle by defining an algebraic CPO structure on the set of trace distributions of A. We also prove limit and convex closure properties of trace distributions in an appropriate metric space.

AB - We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the well-known trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite probabilistic automata and prove that our notion of observational equivalence coincides with the trace distribution equivalence proposed by Segala. Along the way, we give an explicit characterization of the set of probabilistic executions of an arbitrary probabilistic automaton A and generalize the Approximation Induction Principle by defining an algebraic CPO structure on the set of trace distributions of A. We also prove limit and convex closure properties of trace distributions in an appropriate metric space.

KW - CR-F.1.2

KW - CR-F.4.3

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KW - MSC-68Q10

KW - EWI-6949

KW - MSC-68Q75

KW - CR-F.1.1

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KW - MSC-68Q55

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Cheung L, Stoelinga MIA, Vaandrager FW. A Testing Scenario for Probabilistic Processes. Nijmegen: Radboud University Nijmegen, 2006. 49 p. (ICIS; R06002).