The semaphore codes attached to a Turing machine via resets and their various limits

TL;DR

This paper introduces semaphore codes linked to Turing machines through resets, generalizes the concept to infinite cases, and discusses potential implications for the P versus NP problem.

Contribution

It extends semaphore code theory to infinite resets using profinite limits, offering new approaches to computational complexity questions.

Findings

Semaphore codes provide an approximation framework for resets.

Generalization to infinite resets via profinite limits.

Potential implications for P versus NP problem.

Abstract

We introduce semaphore codes associated to a Turing machine via resets. Semaphore codes provide an approximation theory for resets. In this paper we generalize the set-up of our previous paper "Random walks on semaphore codes and delay de Bruijn semigroups" to the infinite case by taking the profinite limit of $k$-resets to obtain $(-\omega)$-resets. We mention how this opens new avenues to attack the P versus NP problem.