Context Free Language Pumping Lemma pushdown automaton

1i) Show that the language B = {w ∈ {0, 1}∗: w = w R ∧ #0(w) = #1(w)} is not a CFL. ii)Hint: Show that B0 = B ∩0∗1∗0∗ is not a CFL, apply the CFL Pumping Lemma iii) explain why the conclusion carries through to B. (2) Design a deterministic one-tape Turing machine M such that L(M) = B0 . A well commented arc-node diagram is expected. Then without using arcs and nodes, sketch the strategy for deciding the same language by a deterministic 2-tape TM M0 that works much faster.