Rudin-Shapiro Sums Via Automata Theory and Logic

TL;DR

This paper presents a unified logical and automata-theoretic framework to analyze Rudin-Shapiro sums, simplifying proofs of classical results and enabling the discovery of new properties.

Contribution

It introduces a novel approach combining logic and automata theory to study Rudin-Shapiro sums, streamlining proofs and extending existing results.

Findings

Unified framework for Rudin-Shapiro sums

Simplified proofs of classical results

New properties of Rudin-Shapiro sums uncovered

Abstract

We show how to obtain, via a unified framework provided by logic and automata theory, many classical results of Brillhart and Morton on Rudin-Shapiro sums. The techniques also facilitate easy proofs for new results.