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This is not a generalization of the above definition, since, for a string ''s'' and distinct characters ''a'', ''b'', Hopcroft's and Ullman's definition implies {''sa''} / {''b''} yielding {}, rather than { ε }.
The left quotient (when defined similar to Hopcroft and Ullman 1979) of a singleton language ''L''<sub>1</sub> and an arbitrary language ''L''<sub>2</sub> is known as [[Brzozowski derivative]]; if ''L''<sub>2</sub> is represented by a [[regular expression]], so can be the left quotient.<ref>{{cite journal| author=Janusz A. Brzozowski| authorlink=Janusz Brzozowski (computer scientist)|title=Derivatives of Regular Expressions| journal=J ACM| year=1964| volume=11| issue=4| pages=481–494| doi=10.1145/321239.321249}}</ref>
==Syntactic relation==
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== References ==
* {{cite book | first1=John E. | last1=Hopcroft | first2=Jeffrey D. | last2=Ullman | title=Introduction to Automata Theory, Languages and Computation | publisher=Addison-Wesley Publishing | ___location=Reading, Massachusetts | year=1979 | isbn=978-0-201-02988-
{{reflist}}
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