3,559 research outputs found
Scattered one-counter languges have rank less than
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 (, resp).
In this paper we confirm the conjecture that one-counter languages have rank
less than
The FC-rank of a context-free language
We prove that the finite condensation rank (FC-rank) of the lexicographic
ordering of a context-free language is strictly less than
On factorisation forests
The theorem of factorisation forests shows the existence of nested
factorisations -- a la Ramsey -- for finite words. This theorem has important
applications in semigroup theory, and beyond. The purpose of this paper is to
illustrate the importance of this approach in the context of automata over
infinite words and trees. We extend the theorem of factorisation forest in two
directions: we show that it is still valid for any word indexed by a linear
ordering; and we show that it admits a deterministic variant for words indexed
by well-orderings. A byproduct of this work is also an improvement on the known
bounds for the original result. We apply the first variant for giving a
simplified proof of the closure under complementation of rational sets of words
indexed by countable scattered linear orderings. We apply the second variant in
the analysis of monadic second-order logic over trees, yielding new results on
monadic interpretations over trees. Consequences of it are new caracterisations
of prefix-recognizable structures and of the Caucal hierarchy.Comment: 27 page
The Rank of Tree-Automatic Linear Orderings
We generalise Delhomm\'e's result that each tree-automatic ordinal is
strictly below \omega^\omega^\omega{} by showing that any tree-automatic linear
ordering has FC-rank strictly below \omega^\omega. We further investigate a
restricted form of tree-automaticity and prove that every linear ordering which
admits a tree-automatic presentation of branching complexity at most k has
FC-rank strictly below \omega^k.Comment: 20 pages, 3 figure
Laver and set theory
In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip
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