Construct a DFA of the language L = { L1 \ L2 }
How can I construct a DFA of the language L = { L1 \ L2 }
The DFA's of L1 and L2 are given, but how can I "substract" one DFA from another? Is this somehow possible with the relative complement http://en.wikipedia.org/wiki/Complement_(set_theory) and DeMorgans Law?
My solution:
To my understanding, the desired DFA can be obtained by using a modified product automaton, as used for the intersection of L1 and L2, but the terminal states have to be defined differently. Instead of making a product state (q_1,q_2) a terminal state if and only if q_1 and q_2 are terminal states in A(L1) and A(L2) respectively, define it to be a terminal state if and only if q_1 is a terminal state and q_2 is not a terminal state.
I'm not quite sure if besides this elementary argument, the result can be applied by the set formulation of De Morgan's law.
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