Observation and Distinction. Representing Information in Infinite Games

TL;DR

This paper compares two finite-state automata-based models for representing imperfect information in infinite games, showing the greater expressiveness of indistinguishability relations and providing a decidable characterization and construction method.

Contribution

It introduces a formal comparison between observation-based and indistinguishability-based models, establishing the latter's superior expressiveness and providing a decision procedure for finite-state representation.

Findings

Indistinguishability relations are strictly more expressive than observation-based models.

A decidable characterization of representable indistinguishability relations is provided.

A procedure to construct a finite-state observation function from indistinguishability relations is developed.

Abstract

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.