Construct a pda


#1

construct a pda accepting {anbman | m,n>1} by null store.
construct the corresponding context-free accepting the same set.


#2

Following transitions of pushdown automata will do the work:
δ(q0,a,ԑ)=(q1,ax)
δ(q1,a,ax)=(q1,aax)
δ(q1,a,a)=(q1,aa)
δ(q1,b,a)=(q2,a)
δ(q2,b,a)=(q3,a)
δ(q3,b,a)=(q3,a)
δ(q3,a,a)=(q4,ԑ)
δ(q4,a,a)=(q4,ԑ)
δ(q4,a,ax)=(qf,ԑ)
Here, I am checking that the values of m and n remains greater than 1. Also I insert all the 'a’s into the stack and then pop out all the 'a’s when they come after ‘b’ to ensure equal no. of 'a’s at the beginning and the end of the string.