Scattered one-counter languges have rank less than $\omega^2$

Szabolcs Ivan

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arXiv · 2007.00090

Scattered one-counter languges have rank less than $\omega^2$

Szabolcs Ivan

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Abstract

A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is known that scattered context-free (regular, resp.) orderings have rank less than $\omega^\omega$ ($\omega$, resp). In this paper we confirm the conjecture that one-counter languages have rank less than $\omega^2$.

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Szabolcs Ivan. 2020-06-30. Scattered one-counter languges have rank less than $\omega^2$. https://arxiv.org/abs/2007.00090

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