Let Σ be an alphabet, # a symbol not in Σ.

Let x1x2x|x|,y1y2y|y|,z1z2z|z|, be n words over Σ*. Let l denote the maximum length.

The convolution of these words is


where for any i>|w|, the wi is #. This is a new word in ((Σ{#})n)*.

The convolution of x,y,z, is sometimes denoted conv(x,y,z,), or xyz


The convolution of and,fish,be is



This definition bears no to the notion of convolution ( of functions.

Title convolution
Canonical name Convolution1
Date of creation 2013-03-22 14:16:51
Last modified on 2013-03-22 14:16:51
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Definition
Classification msc 68Q45
Classification msc 68Q70
Classification msc 68R15
Related topic Language
Related topic KleeneStar