Editing Zipping (computer science) (section)

== Definition ==
Let &Sigma; be an [[Alphabet (computer science)|alphabet]], # a symbol not in &Sigma;.

Let ''x''<sub>1</sub>''x''<sub>2</sub>... ''x''<sub>|''x''|</sub>, ''y''<sub>1</sub>''y''<sub>2</sub>... ''y''<sub>|''y''|</sub>, ''z''<sub>1</sub>''z''<sub>2</sub>... ''z''<sub>|''z''|</sub>, ... be ''n'' [[word (formal language theory)|words]] (i.e. finite [[sequence]]s) of elements of &Sigma;. Let <math>\ell</math> denote the length of the longest word, i.e. the maximum of |''x''|, |''y''|, |''z''|, ... .

The zip of these words is a finite sequence of ''n''-tuples of elements of {{math|(&Sigma; ∪ {#})}}, i.e. an element of <math>((\Sigma\cup\{\# \})^n)^*</math>:

:<math> (x_1,y_1,\ldots)(x_2,y_2,\ldots)\ldots(x_\ell,y_\ell,\ldots)</math>,

where for any index {{math|''i'' > {{abs|''w''}}}}, the ''w<sub>i</sub>'' is #.

The zip of ''x, y, z, ...'' is denoted zip(''x, y, z, ...'') or ''x'' ⋆ ''y'' ⋆ ''z'' ⋆ ...

The inverse to zip is sometimes denoted unzip.

A variation of the zip operation is defined by:

:<math> (x_1,y_1,\ldots)(x_2,y_2,\ldots)\ldots(x_{\underline{\ell}},y_{\underline{\ell}},\ldots)</math>
 
where <math>\underline{\ell}</math> is the ''minimum'' length of the input words.  It avoids the use of an adjoined element <math>\#</math>, but destroys information about elements of the input sequences beyond <math>\underline{\ell}</math>.