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Limit-Deterministic Büchi Automata for Linear Temporal Logic

  • Salomon Sickert
  • Javier Esparza
  • Stefan Jaax
  • Jan Křetínský
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9780)

Abstract

Limit-deterministic Büchi automata can replace deterministic Rabin automata in probabilistic model checking algorithms, and can be significantly smaller. We present a direct construction from an LTL formula \(\varphi \) to a limit-deterministic Büchi automaton. The automaton is the combination of a non-deterministic component, guessing the set of eventually true \({\mathbf {G}}\)-subformulas of \(\varphi \), and a deterministic component verifying this guess and using this information to decide on acceptance. Contrary to the indirect approach of constructing a non-deterministic automaton for \(\varphi \) and then applying a semi-determinisation algorithm, our translation is compositional and has a clear logical structure. Moreover, due to its special structure, the resulting automaton can be used not only for qualitative, but also for quantitative verification of MDPs, using the same model checking algorithm as for deterministic automata. This allows one to reuse existing efficient implementations of this algorithm without any modification. Our construction yields much smaller automata for formulas with deep nesting of modal operators and performs at least as well as the existing approaches on general formulas.

Keywords

Model Check Markov Decision Process Initial Component Linear Temporal Logic Proof Obligation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors want to thank Orna Kupferman for suggesting the language for proving the lower complexity bound. This work is partially funded by the DFG Research Training Group “PUMA: Programm- und Modell-Analyse” (GRK 1480) and by the Czech Science Foundation Grant No. P202/12/G061.

Supplementary material

428290_1_En_17_MOESM1_ESM.zip (3.2 mb)
Supplementary material 1 (zip 3281 KB)

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Salomon Sickert
    • 1
  • Javier Esparza
    • 1
  • Stefan Jaax
    • 1
  • Jan Křetínský
    • 1
  1. 1.Technische Universität MünchenMunichGermany

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