Scattered context-free linear orderings
英文摘要：
We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a well-ordering.
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The order type of scattered context-free orderings of rank one is computable
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 the isomorphism problem of scattered context-free orderings is undecidable, if one of them has a rank at least two. In this paper we show that it is decidable whether a context-free ordering has rank at most one, and if so, its order type is effectively computable.
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Scattered one-counter languges have rank less than $ω^2$
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 $ω^ω$ ($ω$, resp). In this paper we confirm the conjecture that one-counter languages have rank less than $ω^2$.
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We show that if a context-free grammar generates a language whose lexicographic ordering is well-ordered of type less than $ω^2$, then its order type is effectively computable.
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可构造词刻画由散布线性序索引的词的有理语言
Constructible Words Characterize Rational Languages of Words Indexed by Scattered Linear Orderings
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