Generalized Post Embedding Problems

TL;DR

This paper investigates the decidability of generalized post embedding problems, extending the regular post embedding problem with partial directness and co-directness, and explores the effects of combining these properties.

Contribution

It introduces decidability results for extended post embedding problems with partial directness and co-directness, and demonstrates undecidability when combining these properties.

Findings

Decidability of the regular post embedding problem extended with partial directness.

Decidability results for universal and counting versions.

Undecidability when combining directness and co-directness.

Abstract

The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to undecidability.