| dbpprop:abstract
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- In computer science, specifically formal languages, convolution is a function which maps a tuple of sequences into a sequence of tuples. It is defined as follows: Let Σ be an alphabet, # a symbol not in Σ. Let x1x2... x|x|, y1y2... y|y|, z1z2... z|z|, ... be n words over Σ; i.e. sequences of elements of Σ. Let <math>\ell</math> denote the maximum length. The convolution of these words is <math> (x_1,y_1,\ldots)(x_2,y_2,\ldots)\ldots(x_\ell,y_\ell,\ldots)</math> where for any index i > |w|, the wi is #. This is a new word in <math>(^n)^*</math>. The convolution of x, y, z, ... is denoted conv(x, y, z, ... ), zip(x, y, z, ... ) or x ⋆ y ⋆ z ⋆ ... The inverse to convolution is sometimes denoted unzip. A variation of the convolution 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>.
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| rdfs:comment
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- In computer science, specifically formal languages, convolution is a function which maps a tuple of sequences into a sequence of tuples. It is defined as follows: Let Σ be an alphabet, # a symbol not in Σ. Let x1x2... x|x|, y1y2... y|y|, z1z2... z|z|, ... be n words over Σ; i.e. sequences of elements of Σ. Let <math>\ell</math> denote the maximum length.
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![[RDF Data]](/statics/sw-cube.png)
