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Büchi Objectives in Countable MDPs (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke

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Author Details

Stefan Kiefer
  • University of Oxford, UK
Richard Mayr
  • University of Edinburgh, UK
Mahsa Shirmohammadi
  • CNRS, Paris, France
  • IRIF, Paris, France
Patrick Totzke
  • University of Liverpool, UK

Funding

  • Kiefer, Stefan: Supported by a Royal Society University Research Fellowship.
  • Mayr, Richard: Supported by EPSRC grant EP/M027651/1.
  • Shirmohammadi, Mahsa: Supported by PEPS JCJC grant AAPS.

Acknowledgements

The authors thank anonymous reviewers for their helpful comments.

Cite AsGet BibTex

Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, and Patrick Totzke. Büchi Objectives in Countable MDPs (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 119:1-119:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICALP.2019.119

Abstract

We study countably infinite Markov decision processes with Büchi objectives, which ask to visit a given subset F of states infinitely often. A question left open by T.P. Hill in 1979 [Theodore Preston Hill, 1979] is whether there always exist epsilon-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so far. We provide a negative answer to this question by constructing a non-trivial counterexample. On the other hand, we show that Markov strategies with only 1 bit of extra memory are sufficient.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Probability and statistics
Keywords
  • Markov decision processes

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