Fill in the correspondences between languages, grammars and machines Type Language Machine Example of Language in Type n, but not in Type n+1 Type 1 Type-2 Type-3 n/a Define the following functions for the respective machines. The first one is done as an example Machine Transition Function Extended Transition Function , Computation DFA NFA NFA-A PDA LBA TM (standard TM State whether each of the following classes of languages is closed under the indicated operation Operation Regular Context Free Context- Recursive Recursively Enumerable Union Intersection Complement Concatenation Kleene Star Reversal Homomorphism For each ofthe following grammars, dicate preferably using a regular expression over N. andor the acceptable format for the left and right-hand-sides of the production rules Grammar LHS RHS Regular Left-Linear Right-Linear Context-Free Chomsky Normal Form Greibach Normal Fornm Context-Sensitive Unrestricted Semi- Thue system