Let $\Sigma$ be an alphabet, $\#$ a symbol not in $\Sigma$.

Let $x_{1}x_{2}\ldots x_{{|x|}},y_{1}y_{2}\ldots y_{{|y|}},z_{1}z_{2}\ldots z_{{|z|}},\ldots$ be $n$ words over $\Sigma^{*}$. Let $l$ denote the maximum length.

The convolution of these words is

where for any index $i>|w|$, the $w_{i}$ is $\#$. This is a new word in $((\Sigma\cup\{\#\})^{n})^{*}$.

The convolution of $x,y,z,\ldots$ is sometimes denoted conv($x,y,z,\ldots$), or $x\star y\star z\star\ldots$