1. Regular Expression to NFA
Module 05.1 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

2. RE to NFA
So far,
RGR RGL Minimum
DFA
RE NFA DFA
Done
Soon
Now

3. RE to NFA Algorithm 1 (bottom-up): Recursively build the FSA,
Mimicking structure of the RE.
Each FSA built has one start state, and one final state.
Conversions:
if ø,
if ℇ, and
if a. 2 1 1 1 2 a

4. RE to NFA
if P + Q,
or if PQ, and
if P*. 1 ε Q P 2 P Q ε 1 2 1 P ε 2

5. RE to NFA example: (b (aba + ε) a)* b a b a a 3 7 a b ε 1 2 3 4 5 6 78 a 9 10 11 a 3 4 5 6 7 8 a b ε

6. RE to NFA (b (aba + ε) a)* 3 7 a b ε 3 7 a b ε 9 12 3 7 a b ε 9 12 4 56 7 8 a b ε 3 4 5 6 7 8 a b ε 13 9 12 3 4 5 6 7 8 a b ε 13 9 12 2 1

7. 3 4 5 6 7 8 a b ε 13 9 12 2 1
RE to NFA
(b (aba + ε) a)* 3 4 5 6 7 8 a b ε 13 9 12 2 1 10 11 2 12 3 4 6 7 ε a 8 13 14 1 b 10 5 9 11 15

8. Algorithm 2 (top-down): 4 Rules Start: Apply Rules:
RE to NFA
Algorithm 2 (top-down): 4 Rules
Start:
Apply
Rules: E a a* ε ab a b b
a + b a

9. RE to NFA Example (a + b)* (aa + bb) (a + b)* aa + bb aa a + b ε bb ε

10. RE to NFA (another Example)
ba(a + b)* ab b a ε

11. summary Algorithm 1: Builds FSA bottom up Good for machines
Bad for humans
Algorithm 2:
Builds FSA top down
Bad for machines
Good for humans

12. RE to NFA So far, RGR RGL Minimum DFA RE NFA DFA Two algorithms Done
Soon
Two algorithms