Consensus Game Acceptors and Iterated Transductions

TL;DR

This paper introduces a game-based acceptor model that characterizes context-sensitive languages and explores its expressiveness through iterated transductions, revealing connections to context-free languages.

Contribution

It establishes a novel game-theoretic framework for recognizing formal languages and links it to well-known language classes via transductions.

Findings

Consensus game acceptors characterize context-sensitive languages.

A subclass of these games characterizes context-free languages.

The model connects language recognition with iterated transductions.

Abstract

We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input words correlated by a finite graph. The players have a joint objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input. We show that the acceptor model based on consensus games characterises context-sensitive languages. Further, we describe the expressiveness of these games in terms of iterated synchronous transductions and identify a subclass that characterises context-free languages.