Tensor Product Representations of Subregular Formal Languages

TL;DR

This paper introduces a geometric and tensor-based framework to characterize subregular classes of regular languages using finite model theory and logical structures.

Contribution

It presents a novel approach that compiles logical descriptions of subregular languages into tensor structures for analysis.

Findings

Tensor structures effectively represent subregular language classes.

Logical characterizations can be translated into geometric tensor models.

The method applies to specific subregular languages over different models.

Abstract

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over these models define subregular classes of languages. The semantics of such statements can be compiled into tensor structures, using multilinear maps as function application for evaluation. This method is applied to consider two properly subregular languages over different string models.