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Design a PDA which recognizes the language
Problem
Generate the push down automata (PDA) that recognizes the language E={aibj| i is not equal to j and I is not equal to 2j}.
Solution
Consider the two languages as given below −
L1={aibj|i,j>=0 and i>2j}L2={aibj|i,j>=0 and i<2j}
Convince yourself that L=L1UL2
In L1, the number of a's are more than double of b's so L1 as follows −
S1->aA
A->aaAb|aA|epsilon
In L2, the number of a's are less than double the number of b's
So the CFG for L2 becomes as follows −
S2->Bb|aBb
B->Bb|aBb|aaBb|epsilon
S->S1|S2
L1: {aibj:i>2j}
L2:{aibj: i<2j}
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