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P, O, R be regular expression over ∑, P is not ε, then R=Q + RP has a unique solution:(a) Q*P(b) QP*(c) Q*P*(d) (P*O*)*I got this question during an interview for a job.Asked question is from Operators of Regular Expression in chapter Regular Expressions and Languages of Automata Theory |
Answer» CORRECT answer is (b) QP* To elaborate: The given statement is the Arden’s Theorem and it tends to have a UNIQUE solution as QP*. Let P and Q be regular expressions, R=Q+RP R=Q+(Q+RP) P R=Q+((Q+RP) +RP) +P=Q+QP+RPP+RPP=Q+QP+(Q+RP) PP+(Q+RP) PP=Q+QP+QPP+RPPP+QPP+RPPP, If we do this recursively, we GET: R= QP* |
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