Classify the following sets as finite, decidable, regular, context-free, or undecidable, and name the corresponding automata discussed in this course. Justify your answers.

(a) {0^m1ⁿ | m n}

(b) 11^*(0|11)^*

(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