Left quotient

In mathematics and computer science, the right quotient (or simply quotient) of a formal language L 1 {displaystyle L_{1}} with a formal 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}} . In symbols, we write: In mathematics and computer science, the right quotient (or simply quotient) of a formal language L 1 {displaystyle L_{1}} with a formal 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}} . In symbols, we write: In other words, each string in L 1 / L 2 {displaystyle L_{1}/L_{2}} is the prefix of a string w x {displaystyle wx} in L 1 {displaystyle L_{1}} , with the remainder of the word being a string in L 2 {displaystyle L_{2}} . Similarly, the left quotient of L 1 {displaystyle L_{1}} with L 2 {displaystyle L_{2}} is the language consisting of strings w such that xw is in L 2 {displaystyle L_{2}} for some string x in L 1 {displaystyle L_{1}} . In symbols, we write: The left quotient can be regarded as the set of postfixes that complete words from L 2 {displaystyle L_{2}} , such that the resulting word is in L 1 {displaystyle L_{1}} .