NPTEL Theory of Computation Assignment 3 Answer

Consider the following DFA:

Which of the following pairs of states is a pair of equivalent states ?

Consider the relation p≈qp≈q defined as x∈Σ∗x∈Σ∗ δ(p,x)∈F⟺δ(q,x)∈Fδ(p,x)∈F⟺δ(q,x)∈F , defined for a DFA (Q,Σ,δ,q0,F)(Q,Σ,δ,q0,F)Which of the following statements is correct?

Consider a DFA (Q,Σ,δ,q0,F)(Q,Σ,δ,q0,F).  Let p∈Qp∈Q,  a∈Σa∈Σ and y∈Σ∗y∈Σ∗, which of the following is always same as  δ(δ(p,y),a)δ(δ(p,y),a) ?

Which of the following languages defined over {a,b}∗{a,b}∗ is regular ?

Consider a regular language L over {0,1}∗{0,1}∗, which of the following languages are regular? (Rev(w) is reverse of string w)(Rev(w) is reverse of string w)

Suppose pumping lemma in the contra-positive form is being applied on the language L={0m1n|m>n}L={0m1n|m>n} in order to prove that it is not regular. Given p (refer to pumping lemma), which of the following could be the choice of string from L of length at least p in order to proceed.

Continuing from the previous question, given any partition of the selected string xyz such that |xy|≤p and |y|>0|xy|≤p and |y|>0, which one of the following should be the choice of i, where i≥0i≥0 such that xyizxyiz is not in L.