Streaming Rewriting Games: Winning Strategies and Complexity

TL;DR

This paper explores the one-pass setting of context-free rewriting games, analyzing strategies and computational complexity when players have limited information and must proceed sequentially.

Contribution

It introduces the one-pass model for context-free games, characterizes conditions for strategy existence, and studies the complexity of related decision problems.

Findings

Conditions for the existence of dominant strategies identified

Complexity results for strategy decision problems established

Insights into sequential, incomplete-information game dynamics provided

Abstract

Context-free games on strings are two-player rewriting games based on a set of production rules and a regular target language. In each round, the first player selects a position of the current string; then the second player replaces the symbol at that position according to one of the production rules. The first player wins as soon as the current string belongs to the target language. In this paper the one-pass setting for context-free games is studied, where the knowledge of the first player is incomplete, she selects positions in a left-to-right fashion and only sees the current symbol and the symbols from previous rounds. The paper studies conditions under which dominant or undominated strategies for the first player exist and investigates the complexity of some related algorithmic problems.