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# Subsequence

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 Title: Subsequence Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Subsequence

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 \langle A,B,D \rangle is a subsequence of \langle A,B,C,D,E,F \rangle . They should not be confused with substring which is \langle A,B,C,D \rangle for above string and which is a refinement of subsequence.

## Contents

• Common subsequence 1
• Applications 2
• Theorems 3
• Notes 5

## 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

X = \langle A,C,B,D,E,G,C,E,D,B,G \rangle and
Y = \langle B,E,G,C,F,E,U,B,K \rangle

then a common subsequence of X and Y could be

G = \langle B,E,E \rangle.

This would not be the longest common subsequence, since G only has length 3, and the common subsequence \langle B,E,E,B \rangle has length 4. The longest common subsequence of X and Y is \langle B,E,G,C,E,B \rangle .

## 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.

## Notes

1. ^ In computer science,