DFA MINIMIZATION Maham Noor 4/8/20171

Content: Method 1 Equivalence Theorem Method 2 Table filling method 2

Introduction Minimization/optimization of a deterministic finite automaton refers to the detection of those states of a DFA, whose presence or absence in a DFA does not affect the language accepted by the automata. The states that can be eliminated from automata, without affecting the language accepted by automata, are: Unreachable or inaccessible states. Dead states. 3

Example of unreachable state

Example of dead state

Equivalence Theorem Consider the following DFA Steps: 1) Draw transition table 2) Find 0, 1, 2 ….equivalence

Step 01: Transition Table

Step 02: Find equivalence 0 Equivalence {A,B,C,D} {E} 1 Equivalence {A,B,C} {D} {E} 2 Equivalence {A,C} {B} {D} {E} 3 Equivalence {A,C} {B} {D} {E}

Step 03: equivalence to minimized DFA 0 Equivalence {A,B,C,D} {E} 1 Equivalence {A,B,C} {D} {E} 2 Equivalence {A,C} {B} {D} {E} 3 Equivalence {A,C} {B} {D} {E}

Example 02 Consider the following transition table Steps: 1) Find 0, 1, 2 ….equivalence

Step 01: find 0,1,2…. Equivalence 0 Equivalence {qo, q1, q2, q3, q4, q5, q6, q7}{q2} 1 Equivalence {q0, q4, q6} {q1, q7} {q3, q5} {q2} 2 Equivalence {q0, q4} {q6} {q1, q7} {q3, q5} {q2} 3 Equivalence {q0, q4} {q6} {q1, q7} {q3, q5} {q2}

01 q0q1q5 q1q6q2 q0q2 q3q2q6 q4q7q5 q2q6 q4 q7q6q2 01qo, q4q1, q7q3, q5 q6 q0, q4 q1, q7q6q2 q3, q5q2q6 q2q0, q4q2