A set S of nonnegative integers is called an arithmetic progresion if there exist some integers n and p such thatS = {n + ip : i  0}Let A  {a} and consider S = {| x |: x  A}.(1) Show that if S is an arithmetic progression, then A can be recognized by aDFA(2) Show that if A can be recognized by a DFA, then S is the union of a nite number of arithmetic
Show that if S is an arithmetic progression, then A can be recognized by a DFA
finite automata