Local generation of languages: the monotonic binary sequences

TL;DR

This paper investigates the local generation of binary monotonic sequences using simplicial complexes, providing theoretical results and classifying minimal complexes that generate such languages.

Contribution

It introduces a detailed study of local language generation for binary monotonic sequences and identifies classes of minimal simplicial complexes responsible for this process.

Findings

Proves general results on local language generation.

Identifies classes of minimal simplicial complexes.

Provides a theoretical framework for understanding local generation.

Abstract

In a previous article, we have introduced the problem of local generation of languages, where the communication underlying the generation procedure is captured by a simplicial complex. We study in details this problem for the language of binary monotonic sequences. We prove general results and identify several classes of minimal simplicial complexes generating this language.