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Left quotient

If $L 1$ and $L 2$ are formal languages, then the left quotient of $L 1$ with $L 2$ is the language consisting of strings w such that xw is in $L 1$ for some string x in $L 2$ . In symbols, we write:

$L_1 / L_2 = \{w \ | \ \ \exists x \in L_2 \ \ : \ \ xw \in L_1\}$

You can regard the left quotient as the set of postfixes that complete words from $L 2$ , such that the resulting word is in $L 1$ .

For more details, see right quotient.

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09-23-2007 01:00:40
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Left quotient