Consider the finite automaton given by the diagram. Is this automaton deterministic? Using a standard method construct a regular expression for the language defined by the automaton. A C a,b B D b Minimize the DFA with the set of states {1, 2, 3, 4, 5, 6, 7, 8), input alphabet = {a, b} initial state 1, final states {3, 4) and the transition function given by the table: a b 1 2 62 36 3F 2 4 4F 5 3 a b 5 4 1 615 718 887 Let L be the language accepted by this DFA. Consider the equivalence relation R, on * (thus R = * x *) defined by: xRLy if and only if for all z E *, xz E L iff yz L. What is the index (the number of equivalence classes) of R? Describe precisely at least one of the equivalence classes of R. (by giving an automaton, or a regular expression).