Question

2. (15) Show using a cross-product construction that the class of regular languages is closed under set difference. You do not need an inductive proof, but you should convincingly explain why your construction works.

Answer 1

0 solution: Given that using a mass -pooduct constouction that the class of relax lasquggoro is ched unto col dipercre. you do not need an inductive pooof, but you should convincingly Espain wou jouet construction wooko. set diffcoence operation defers to the operalion which includes He Fogd opecalon beet Scould not pctfoon the sacord pocoation. Suppose Thebe ate 2 The DFA Foo ABC ogrelat languages A and B. Ford The DFA Foo B be : Z z z Z T Ta Tr There are m. states in А and notates in B. Then the cooos pooduct will have mªn states.

Z Z M sorting Symbol p the and in the second OFA, state Tk on The coooo pooduct constouction takes pace ao follows :- The Transition in the scrillant OfA of the. A-B will be If in the post ofa, slate gi ori to state Th. seeing gymbol p goes Then in the new DFA of get difference. The Hale [Bf Tk] on seting gostal p goes to stale (3) , ta] The articl state will be the sale comprising initial state of frost and second DFA that is state [51 Ti] As per definition of del diffeserce. The degulat lagjuage A-5 will accept those stoings cohich ace pack Of A biel not Bo Then, in the coultant OfA. The final state will be com o whobe To Do any non firal slale of the second fa. since in the coultant OFA, The statco que defined using the coors pooduct of the 2 DFAJ The initial stałe, Final state and The loansition Function is aloo defined and the alphabet input demains the same the weste land language is a ojedat lagugge. using a coax-poodect condouction it can be pooved Hal the class of agjelat languages is closed undo set di frescace. Henc

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