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regular-language

A regular expression for the complement of the language L

Let L(R) be the language denoted by regular expression R.

I'd really love your help with presenting a regular expression to the complement

of L((0 U 10 U 110)* (epsilon U 1 U 11)), where language is over the alphabet {0,1}, epsilon is the empty word, 'U' stands for union and '*' is the star iterator.

I tried to find it with De Morgan's laws. I think that I am requested to evaluate

not (L((0 U 10 U 110)* (epsilon U 1 U 11)))- what is not of the '*' for example?

Thanks a lot

Solution

  • You need to convert the regular expression to a deterministic finite automaton, complement that (into another DFA), then turn that back into a regular expression.