B\"uchi VASS recognise w-languages that are Sigma^1_1 - complete

TL;DR

This paper demonstrates that a specific class of complex, non-regular languages known as Sigma^1_1-complete can be recognized by simple automata with a single blind counter, expanding understanding of their computational power.

Contribution

It provides the first example of a Sigma^1_1-complete language recognized by a B"uchi VASS with only one place, showing increased recognition capabilities of simple automata.

Findings

Sigma^1_1-complete languages can be recognized by one blind counter B"uchi automata.

Single-place B"uchi VASS have greater expressive power than previously known.

The result bridges automata theory and descriptive set theory in the context of infinite words.

Abstract

This short note exhibits an example of a Sigma^1_1-complete language that can be recognised by a one blind counter B\"uchi automaton (or equivalently a B\"uchi VASS with only one place).