منابع مشابه
Unavoidable and Almost Unavoidable Sets of Words
A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length.
متن کاملUnavoidable Sets of Partial
The notion of an unavoidable set of words appears frequently in the fields of mathematics and theoretical computer science, in particular with its connection to the study of combinatorics on words. The theory of unavoidable sets has seen extensive study over the past twenty years. In this paper we extend the definition of unavoidable sets of words to unavoidable sets of partial words. Partial w...
متن کاملUnavoidable Sigma–Porous Sets
We prove that every separable metric space which admits an `1tree as a Lipschitz quotient, has a σ-porous subset which contains every Lipschitz curve up to a set of 1-dimensional Hausdorff measure zero. This applies to any Banach space containing `1. We also obtain an infinite-dimensional counterexample to the Fubini theorem for the σ-ideal of σ-porous sets.
متن کاملUnavoidable Sets of Constant Length
A set of words X is called unavoidable on a given alphabet A if every infinite word on A has a factor in X. For k, q ≥ 1, let c(k, q) be the number of conjugacy classes of words of length k on q letters. An unavoidable set of words of length k on q symbols has at least c(k, q) elements. We show that for any k, q ≥ 1 there exists an unavoidable set of words of length k on q symbols having c(k, q...
متن کاملOn Unavoidable Sets of Word Patterns
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under con...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2006
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2006.03.024