A pumping-like lemma for languages over infinite alphabets

TL;DR

This paper introduces a pumping lemma for languages over infinite alphabets accepted by one-register alternating automata, showing that their word length sets are semi-linear, which advances understanding of their structural properties.

Contribution

It presents a novel pumping lemma for a specific class of automata over infinite alphabets, establishing semi-linearity of their word length sets.

Findings

Languages accepted by these automata have semi-linear length sets

The pumping lemma provides structural insights into such languages

Advances theoretical understanding of automata over infinite alphabets

Abstract

We prove a kind of a pumping lemma for languages accepted by one-register alternating finite-memory automata. As a corollary, we obtain that the set of lengths of words in such languages is semi-linear.