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 .

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, 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.

[ Substring vs. subsequence

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.^[1]

[ See also

• Subsequential limit
• Limit superior and limit inferior
• Longest increasing subsequence problem
• Erdős–Szekeres theorem

[ References

1. ^ Gusfield, Dan (1999) [1997]. Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. USA: Cambridge University Press. pp. 4. ISBN 0-521-58519-8. 

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