Emergent Mind
Scattered one-counter languges have rank less than $ω^2$
(2007.00090)
Published Jun 30, 2020
in
cs.FL
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 $\omega2$.
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