ISI2011-CS-4b
Suppose $M = (Q, \Sigma, \delta, q_0, F)$ is a deterministic finite automaton, and suppose there exists a state $q \in Q$, a string $z \in \Sigma$, and integers $i, j > 0$ such that $\delta(q, z^i) = \delta(q, z^j) = q$. Prove that $\delta(q, z^{\gcd(i,j)}) = q.$
Suppose $M = (Q, \Sigma, \delta, q_0, F)$ is a deterministic finite automaton, and suppose there exists a state $q \in Q$, a string $z \in \Sigma$, and integers $i, j 0$...
