User:Jshflynn/Definition:Left quotient language

Definition

Let $L$ and $K$ be two languages over an alphabet $\Sigma$.

Then the left quotient of $L$ by $K$ is denoted $L^{-1}K$ and is defined as the set:

$$\{x \in \Sigma^*: y \circ x \in K \text{ for some } y \in L \}$$

Where $\circ$ denotes concatenation and $\Sigma^*$ denotes the Kleene star of $\Sigma$.