Rational functions via recursive schemes

TL;DR

This paper introduces a novel way to characterize rational string functions using order-preserving interpretations within a weak monadic programming language, refining previous characterizations based on MSO interpretations.

Contribution

It provides a new characterization of rational functions through order-preserving interpretations, enhancing the understanding of their structure in formal language theory.

Findings

New characterization of rational functions using order-preserving interpretations

Refinement of previous MSO-based characterizations

Connections established between formal language theory and monadic programming

Abstract

We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of rational functions by order-preserving MSO interpretations.