a$)$ Let $L=\{a^i{b}^j{c}^k|k>i,j>2k,i>0\}.$ Compute the type for the given language $L$ through Chomsky hierarchy

and suggest the possible machine which can validate the members of the language L$.(5$ marks$)$

b$)$ State whether the instances with $=\{a,b\}$ of the Post Correspondence Problem $($PCP$)$ have a solution. The

following are the instances M$($ ab$,$bab, bbaaa $)$ and N $=($a$,$ba$,$bab$).$in ase pcp has a solution.describe post correspondane solution with justification