On certain one-counter shifts

TL;DR

This paper introduces a new class of one-counter shifts derived from a nonsofic shift example, expanding the understanding of shift classes beyond standard one-counter shifts.

Contribution

It describes a novel class of one-counter shifts that are distinct from the standard ones, based on extrapolations from a specific nonsofic shift example.

Findings

Identifies a new class of one-counter shifts

Demonstrates these shifts are disjoint from standard one-counter shifts

Provides a framework for analyzing nonsofic shift systems

Abstract

Extrapolating from the two-block system of an example of a nonsofic shift hat was given by Lind and Marcus, a class of one-counter shifts is described, that is disjoint from the class of standard one-counter shifts.