Observation and Distinction. Representing Information in Infinite Games

Authors Dietmar Berwanger, Laurent Doyen

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Dietmar Berwanger
  • LSV, CNRS & ENS Paris-Saclay, France
Laurent Doyen
  • LSV, CNRS & ENS Paris-Saclay, France

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Dietmar Berwanger and Laurent Doyen. Observation and Distinction. Representing Information in Infinite Games. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata. The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Representations of games and their complexity
  • Computing methodologies → Reasoning about belief and knowledge
  • Computing methodologies → Planning under uncertainty
  • Infinite Games on Finite Graphs
  • Imperfect Information
  • Automatic Structures


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