Deciding What Is Good-For-MDPs

Authors Sven Schewe , Qiyi Tang , Tansholpan Zhanabekova

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Sven Schewe
  • University of Liverpool, UK
Qiyi Tang
  • University of Liverpool, UK
Tansholpan Zhanabekova
  • University of Liverpool, UK


We thank the anonymous reviewers of this paper for their constructive feedback. We thank an anonymous reviewer for raising the excellent question (to the original version) of whether or not QGFM and GFM are different. They proved not to be. Without their clever question, we would not have considered this question, and thus not strengthened this paper accordingly.

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Sven Schewe, Qiyi Tang, and Tansholpan Zhanabekova. Deciding What Is Good-For-MDPs. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Nondeterministic good-for-MDPs (GFM) automata are for MDP model checking and reinforcement learning what good-for-games automata are for reactive synthesis: a more compact alternative to deterministic automata that displays nondeterminism, but only so much that it can be resolved locally, such that a syntactic product can be analysed. GFM has recently been introduced as a property for reinforcement learning, where the simpler Büchi acceptance conditions it allows to use is key. However, while there are classic and novel techniques to obtain automata that are GFM, there has not been a decision procedure for checking whether or not an automaton is GFM. We show that GFM-ness is decidable and provide an EXPTIME decision procedure as well as a PSPACE-hardness proof.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Mathematics of computing → Markov processes
  • Büchi automata
  • Markov Decision Processes
  • Omega-regular objectives
  • Reinforcement learning


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