On optimum left-to-right strategies for active context-free games

TL;DR

This paper investigates the computational complexity of determining whether all safely rewritable strings in active context-free games can be rewritten using a left-to-right strategy, revealing EXPSPACE-completeness and EXPTIME-completeness results.

Contribution

It establishes the complexity of deciding left-to-right rewriting strategies in active context-free games, including the case with finite replacement languages.

Findings

Deciding left-to-right strategies is EXPSPACE-complete for general games.

For games with finite replacement languages, the problem is EXPTIME-complete.

Rewriting problem remains undecidable in general, but specific cases are computationally characterized.

Abstract

Active context-free games are two-player games on strings over finite alphabets with one player trying to rewrite the input string to match a target specification. These games have been investigated in the context of exchanging Active XML (AXML) data. While it was known that the rewriting problem is undecidable in general, it is shown here that it is EXPSPACE-complete to decide for a given context-free game, whether all safely rewritable strings can be safely rewritten in a left-to-right manner, a problem that was previously considered by Abiteboul et al. Furthermore, it is shown that the corresponding problem for games with finite replacement languages is EXPTIME-complete.