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Formal Methods in System Design

, Volume 54, Issue 2, pp 145–163 | Cite as

Statistical verification of PCTL using antithetic and stratified samples

  • Yu WangEmail author
  • Nima Roohi
  • Matthew West
  • Mahesh Viswanathan
  • Geir E. Dullerud
Article
  • 65 Downloads

Abstract

In this work, we study the problem of statistically verifying Probabilistic Computation Tree Logic (PCTL) formulas on discrete-time Markov chains (DTMCs) with stratified and antithetic samples. We show that by properly choosing the representation of the DTMCs, semantically negatively correlated samples can be generated for a fraction of PCTL formulas via the stratified or antithetic sampling techniques. Using stratified or antithetic samples, we propose statistical verification algorithms with asymptotic correctness guarantees based on sequential probability ratio tests, and show that these algorithms are more sample-efficient than the algorithms using independent Monte Carlo sampling. Finally, the efficiency of the statistical verification algorithm with stratified and antithetic samples is demonstrated by numerical experiments on several benchmarks.

Keywords

Markov chains Temporal logic Variance reduction Sequential probability ratio test 

Notes

Acknowledgements

This work was supported by NSF CPS Grant 1329991 and AFOSR Grant FA9550-15-1-0059.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Electrical and Computer EngineeringDuke UniversityDurhamUSA
  2. 2.Computer Science and EngineeringUniversity of California San DiegoSan DiegoUSA
  3. 3.Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  4. 4.Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  5. 5.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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