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单词 PrefixSet
释义

prefix set


Let X be a set, and wX* be a word, i.e. an element of the free monoid on X. A word vX* is called prefix of w when a second word zX* exists such that x=vz. A proper prefix of a word u is a prefix v of u not equal to u (sometimes v is required to be non-empty).

Note that the empty wordPlanetmathPlanetmath ε and w are prefix of w, and a proper prefix of w if w is non-empty.

The prefix set of w is the set pref(w) of prefixes of w, i.e. if w=w1w2wn with wjX for each j{1,,n} we have

pref(w)={ε,w1,w1w2,,w1w2wn-1,w}.

Some closely related concepts are:

  1. 1.

    A set of words is prefix closed if for every word in the set, any of its prefix is also in the set.

  2. 2.

    The prefix closure of a set S is the smallest prefix closed set containing S, or, equivalently, the union of the prefix sets of words in S.

  3. 3.

    A set S is prefix free if for any word in S, no proper prefixes of the word are in S.

Titleprefix set
Canonical namePrefixSet
Date of creation2013-03-22 16:11:56
Last modified on2013-03-22 16:11:56
OwnerMazzu (14365)
Last modified byMazzu (14365)
Numerical id6
AuthorMazzu (14365)
Entry typeDefinition
Classificationmsc 20M05
Definesprefix
Definesprefix set
Definesproper prefix
Definesprefix closed
Definesprefix closure
Definesprefix free
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