1. Visual Kleene’s Theorem Kleene, Inc. Robert Sharpe & Scott White Advisor: Professor Retterer

2. Preview Brief Problem Review User Interface Input Verification Kleene Algorithm Functions Testing Words Finite Automaton Drawing Project Future Conclusion

3. Visual Teaching Tool Kleene’s Theorem Regular Expression (RE) Input Finite Automaton (FA) Output Overview RE ≡ FA ≡ TG ≡ RE

4. For = {a, b} RE  FA - + a,b a b a (a + b)* a,b ab -132 222 +333

5. User Interface Web Form

6. User Interface Windows Form

7. Backus-Naur Form for RE’s Used for RE Format Testing ::= := “+” | “*” | nothing ::= := “.” | nothing ::= | “(“ “)” := “a” | “b” Input Verification

8. Infix-Prefix Conversion Infix  1 + 2 * 3 = 7 vs. 1 + 2 * 3 = 9 (Order of Operations) (Left to Right) Prefix  +1*23 Solves Order of Operations Problem Example

9. Kleene Algorithm Functions Single Letter FA –Single variable –kSingle OR Operation –+ operator –kPlus a r 1 + r 2

10. Kleene Algorithm Functions cont’d Concatenation –. operator –kConcat Kleene Closure –* operator –kStar r 1. r 2 r*

11. Given an RE, what words are accepted? Testing Words Test Words

12. Complex State Drawing Decisions Trade-Off Layout Algorithm vs. User Interaction FA Drawing

13. Sample  Drawing FA Drawing Cont’d

14. Conclusion RE  FA Teaching Tool “Extreme Programming” style 289.95 hours @ $20/hr.=$5799. 00 Future Senior Design Project

15. Questions? Kleene, Inc. Robert Sharpe & Scott White