In mathematics and computer science, the right quotient (or simply quotient) of a language with respect to language is the language consisting of strings w such that wx is in for some string x in .[1] Formally:
In other words, for all the strings in that have a suffix in , the suffix is removed.
Similarly, the left quotient of with respect to is the language consisting of strings w such that xw is in for some string x in . Formally:
In other words, we take all the strings in that have a prefix in , and remove this prefix.
Note that the operands of are in reverse order: the first operand is and is second.
^Linz, Peter (2011). An Introduction to Formal Languages and Automata. Jones & Bartlett Publishers. pp. 104–108. ISBN 9781449615529. Retrieved 7 July 2014.
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