Theory of Computation

1. How would you show conclusively that a certain graphics library, G2, has all the functionality of graphics library G1? 2. Describe two transition-system models of computation and one model that computes functions SS or N N. 3. Classify the following sets as finite, decidable, regular, context-free, or undecidable, and name the corresponding automata. Justify your answers. (a) {0m1nm11 n (b) 11(011) (c) binary representations of prime numbers (d) {(P,x)P is the code for an S-language program that goes into an infinite loop on input x} (e) sets of balanced parentheses