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In mathematics and computer science, the right quotient of a language L 1 {\displaystyle L_{1}} with respect to language L 2 {\displaystyle L_{2}} is the language consisting of strings w such that wx is in L 1 {\displaystyle L_{1}} for some string x in L 2 {\displaystyle L_{2}}. Formally:
In other words, we take all the strings in L 1 {\displaystyle L_{1}} that have a suffix in L 2 {\displaystyle L_{2}} , and remove this suffix.
Similarly, the left quotient of L 1 {\displaystyle L_{1}} with respect to L 2 {\displaystyle L_{2}} is the language consisting of strings w such that xw is in L 1 {\displaystyle L_{1}} for some string x in L 2 {\displaystyle L_{2}}. Formally:
In other words, we take all the strings in L 1 {\displaystyle L_{1}} that have a prefix in L 2 {\displaystyle L_{2}} , and remove this prefix.