User:Jshflynn/Definition:Language product

Definition
Let $\Sigma$ be an alphabet.

Let $V$ and $W$ be formal languages over $\Sigma$.

Then the language product of $V$ with $W$ is denoted $V \circ_L W$ and defined as:


 * $V \circ_L W = \{x \circ y: x \in V \land y \in W\}$

Note
The notation is the same as that of the subalphabet product as the language product is an extension of the definition of subalphabet product and could only be defined after formal language was defined.