Editing Longest common subsequence (section)

=== Prefixes ===
The prefix ''S''<sub>''n''</sub> of ''S'' is defined as the first ''n'' characters of ''S''.<ref>{{cite book
 | last = Xia | first = Xuhua
 | title = Bioinformatics and the Cell: Modern Computational Approaches in Genomics, Proteomics and Transcriptomics
 | url = https://archive.org/details/bioinformaticsce00xiax_984 | url-access = limited | year = 2007
 | publisher = Springer
 | location = New York
 | page = [https://archive.org/details/bioinformaticsce00xiax_984/page/n38 24]
 | isbn = 978-0-387-71336-6
}}</ref>  For example, the prefixes of ''S'' = (AGCA) are
:''S''<sub>0</sub> = ()
:''S''<sub>1</sub> = (A)
:''S''<sub>2</sub> = (AG)
:''S''<sub>3</sub> = (AGC)
:''S''<sub>4</sub> = (AGCA).

Let ''LCS''(''X'', ''Y'') be a function that computes a longest subsequence common to ''X'' and ''Y''.  Such a function has two interesting properties.