The hardness of counting full words compatible with partial words
نویسندگان
چکیده
منابع مشابه
Counting Primitive Partial Words
A word is primitive if it is not a power of another word. The number of primitive words of a fixed length over an alphabet of a fixed size is well known and relates to the Möbius function. In this paper, we investigate the number of primitive partial words which are strings that may contain “do not know” symbols.
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A partial word, sequence over a finite alphabet that may have some undefined positions or holes, is bordered if one of its proper prefixes is compatible with one of its suffixes. The number theoretical problem of enumerating all bordered full words (the ones without holes) of a fixed length n over an alphabet of a fixed size k is well known. In this paper, we investigate the number of bordered ...
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A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate the problem of counting distinct squares in partial words, or sequences over a finite alphabet that may have some “do not know” symbols or “holes” (a ...
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We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter α = −1. We describe how such a series can be computed by finding an appropriate ordinary generating function and applying a certain transformation. We use this technique to find the generating function for the numb...
متن کاملCounting words with Laguerre polynomials
We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of formal sums of Laguerre polynomials. We use this method to find the generating function for k-ary words avoiding any vincular pattern that has only ones. We also give generating functions for k-ary words cyclically avoiding vincular patterns with only ones whose runs...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2013
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2012.04.001