Question

Define a PDA that accepts language L3 = { aⁿb^m | n > 0 and n > m }.

Implement that PDA in JFLAP. Must use JFLAP

Answer 1

The strings accepted by the given language are as follows:-

L3 = {a, aa, aaa, ......, aab, aaab, aaaab, ......, aaabb, aaaabb, aaaaabb,......}

The PDA for the given language L3={aⁿb^m | n>0 and n>m} is as follows:-

First we push all the a's into the stack, then for every 'b' pop the 'a' from the stack, when all the 'b' gets readed then on reading if the top of the stack is a then go to the state q2 by accepting the string, otherwise not. also afte reading all the a's if their is no 'b' present then also go to the state q2 by accepting the string.

Let us take an input string "aaaabb" to check whether the above PDA works or not.

Present state	Input	Stack top symbol	Operation	Next state
q0	a	z	push	q0
q0	a	a	push	q0
q0	a	a	push	q0
q0	a	a	push	q0
q0	b	a	pop	q1
q1	b	a	pop	q1
q1		a	read	q2

Since all the b's get exhausted and the stack still have a's therefore, reach to final state q2 by accepting the string.

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