String operations: Difference between revisions

Revision as of 00:56, 10 November 2017

Revision as of 20:45, 18 November 2017

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Left quotients may be defined similarly, with operations taking place on the left of a string.{{cn|date=August 2017}}

Hopcroft and Ullman (1979) define the quotient ''L''₁/''L''₂ of the languages ''L''₁ and ''L''₂ over the same alphabet is defined as ''L''₁/''L''₂ = { ''s'' | ∃''t''∈''L''₂. ''st''∈''L''₁ }.<ref>Hopcroft, Ullman (1979), Sect.3.2, p.62</ref>

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 }.