Consider the finite-state automaton given by the following transition diagram:

a. Find the 0-, 1-, 2-, and 3-equivalence classes of states of A.
b. Draw the transition diagram for A ¯ , the quotient automaton of A.

(a)

Find the 0−, 1−, 2−and 3− equivalence classes of states of A.

Given information:

Concept used:

Arrow in the given graph played vital role in answer selection.

Calculation:

It is required to find the 0−, 1−, 2−and 3− equivalence classes of states of A.

0− Equivalence classes- Two states are zero equivalent if both are accepting states or both are

non-accepting states. Therefore, the 0− equivalence classes are: {s0, s1, s3, s4},{s2, s5}

1− Equivalence classes- Two states are 1− equivalent if and only if they are

0− equivalent and after input of any symbol, their next state are 0− equivalent. Therefore, the 1− equivalence classes are: {s0,s3,s4}, {s2,s5}, {s1}

2− Equivalence classes- Two states are called 2− equivalent if and only if they are 1− equivalent and after input of any symbol, their next state are 1− equivalent. Therefore, the 2− equivalent classes are: {s5,s2}, {s1}, {s3},{s4},{s0}

3− Equivalence classes- Two states are called 3− equivalent if and only if they are 2− equivalent and after input of any symbol, their next state are 2− equivalent

(b)

Draw the transition diagram for A¯, the quotient automaton of A.