91Ó°ÊÓ

Consider the finite-state automaton \(A\) given by the following transition diagram: a. Find the \(0-1-\), and 2 -equivalence classes of states of \(A\). b. Draw the transition diagram for \(\bar{A}\), the quotient automaton of \(A\).

In \(I\) and 2 let \(\Sigma=\\{x, y\\}\) be an alphabet. 1\. a. Let \(L_{1}\) be the language consisting of all strings over \(\Sigma\) that are palindromes and have length \(\leq 4\). List the elements of \(L_{1}\) between braces. b. Let \(L_{2}\) be the language consisting of all strings over \(\Sigma\) that begin with an \(x\) and have length \(\leq 3\). List the elements of \(L_{2}\).

Input alphabet \(=\\{0,1\\}\); Accepts the set of all strings that start with 101 .