1. Animated Conversion of Regular Expressions to C Code
On the regular expression:
((a⋅ b)|c)*

2. Thompson’s construction
Convert the regular expression to an NFA.

3. Step 1: construct a parse tree for the expression ((a⋅ b)|c)
Step 1: construct a parse tree for the expression ((a⋅ b)|c)* giving each nested expression a unique name. r6 r5 * r3 | r4 r1 ⋅ r2 c a b

4. Step 2: construct NFA for r1.* r3 | r4 r1 ⋅ r2 c a b

5. Step 3: construct NFA for r2.1 2 r6 r5 * b 3 4 r3 | r4 r1 ⋅ r2 c a b

6. Step 4: construct NFA for r3.b 1 2 4 r6 r5 * r3 | r4 r1 ⋅ r2 c a b

7. Step 5: construct NFA for r4.b 1 2 4 r6 r5 * c 5 6 r3 | r4 r1 ⋅ r2 c a b

8. Step 6: construct NFA for r5.b r5 * 1 2 4 𝜀 𝜀 r3 | r4 7 8 𝜀 𝜀 5 6 r1 ⋅ r2 c c a b

9. Step 7: construct NFA for r6.𝜀 a b 1 2 4 𝜀 𝜀 𝜀 𝜀 10 9 7 8 𝜀 𝜀 5 6 c 𝜀

10. Subset construction
Convert the NFA to a DFA.

11. Draw transition table for DFA2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c

12. Add 𝜀-closure(9) as DFA start state2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c
{9, 7, 1, 5, 10} A

13. Mark state A 2 4 1 5 6 7 8 9 b a c 𝜀 10 NFA States DFA State
Next State a b c
{9, 7, 1, 5, 10}
A 

14. Compute 𝜀-closure(move(A, a))2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c
{9, 7, 1, 5, 10}
A  B
{2}

15. Compute 𝜀-closure(move(A, b))2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c
{9, 7, 1, 5, 10}
A  B -
{2}

16. Compute 𝜀-closure(move(A, c))2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c
{9, 7, 1, 5, 10}
A  B - C
{2}
{6, 10, 7, 1, 5}

17. Mark state B 2 4 1 5 6 7 8 9 b a c 𝜀 10 NFA States DFA State
Next State a b c
{9, 7, 1, 5, 10}
A  B - C
{2}
B 
{6, 10, 7, 1, 5}

18. Compute 𝜀-closure(move(A, c))2 4 b 1 a 5 6 c 7 𝜀 8 9 10
NFA States
DFA State
Next State a b c
{9, 7, 1, 5, 10}
A  B - C
{2}
B 
{6, 10, 7, 1, 5}