Consider the alphabet is Σ = {a,b,c}. For each of the following languages, specify if the language is regular or non-regular. You must support your answer: if the language is non- regular, explain why; if the language is regular design a finite automaton that accepts the language. (a) {a²ibi,j≥ 1} (b) {anbmck | n, m, k ≥ 1} (c) {anzn+mcm | n,m ≥ 1}

55. Find a deterministic finite-state automaton that recog- nizes each of these sets. b) {1, 00} a) {0} c) {1" | n = 2, 3, 4, ...} 56. Find a nondeterministic finite-state automaton that recog- nizes each of the languages in Exercise 55, and has fewer states, if possible, than the deterministic automaton you found in that exercise.