Unavoidable Sets of Words of Uniform Length
نویسندگان
چکیده
منابع مشابه
Unavoidable Sets of Partial Words of Uniform Length
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X . Unlike the case of a set of words without holes, the problem of deciding whether or not a given finite set of n partial words over a k-letter alphabet is avoidable is NP-hard, even when we restrict to a set of partial words of uniform len...
متن کاملUnavoidable 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 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 کاملComputing Minimum Length Representations of Sets of Words of Uniform Length
Motivated by text compression, the problem of representing sets of words of uniform length by partial words, i.e., sequences that may have some wildcard characters or holes, was recently considered and shown to be in P. Polynomial-time algorithms that construct representations were described using graph theoretical approaches. As more holes are allowed, representations shrink, and if representa...
متن کاملNumber of holes in unavoidable sets of partial words I
Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2002
ISSN: 0890-5401
DOI: 10.1006/inco.2001.3123