Subsequence

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In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence is a subsequence of . They should not be confused with substring which is a refinement of subsequence.

Common subsequence

Given two sequences X and Y, a sequence G is said to be a common subsequence of X and Y, if G is a subsequence of both X and Y. For example, if

and

then a common subsequence of X and Y could be

This would not be the longest common subsequence, since G only has length 3, and the common subsequence has length 4. The longest common subsequence of X and Y is .

Applications

Subsequences have applications to computer science,[1] especially in the discipline of bioinformatics, where computers are used to compare, analyze, and store DNA strands.

Take two strands of DNA, say:

ORG1 = ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA
and
ORG2 = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA.

Subsequences are used to determine how similar the two strands of DNA are, using the DNA bases: adenine, guanine, cytosine and thymine.

Theorems

See also

Notes

  1. In computer science, string is often used as a synonym for sequence, but it is important to note that substring and subsequence are not synonyms. Substrings are consecutive parts of a string, while subsequences need not be. This means that a substring of a string is always a subsequence of the string, but a subsequence of a string is not always a substring of the string, see: {{#invoke:citation/CS1|citation |CitationClass=book }}

This article incorporates material from subsequence on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.