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2. Converting Regular Expressions into Finite Automata CSE2303 Formal Methods I Lecture 5

3. Overview Questions Kleene’s Theorem Consequences Convert Regular Expressions to NFA-  Convert NFA-  to FA

4. Questions Can every language which is represented by a regular expression be described by a finite automaton? Can every language which is described by a finite automaton be represented by a regular expression? Can every language be represented by a regular expression or a finite automaton?

5. Kleene’s Theorem Any language which can be defined by –Regular Expressions –Finite Automaton –Nondeterministic Finite Automaton (NFA) –NFA-  –Transition Graphs –Generalised Transistion Graphs can be defined by any of the other methods

6. The Complement of Regular Language is a Regular Language Outline of Proof: –Suppose we have a Regular Language. –Therefore we have a regular expression that defines the language. –So, by Kleene’s Theorem, there is a FA that defines this language. –We can convert this FA into one that defines the complement the language. –So, by Kleene’s Theorem, there is a regular expression that defines the complement.

7. Kleene’s Theorem Regular Expression Finite Automaton NFA-  GTG TGNFA

8. How to convert a Regular Expression into a NFA- 

9. Converting Regular Expression to NFA-  Start with the graph. -+ Regular Expression

10. Apply the following rules until all edges are labeled with a letter or . 1. Delete any edge labeled with   Transform any edge like RS R into S

11. 3. Transform any edge like: into R + S R S

12. 4. Transform any edge like: into R* R 

13. 1- a b  23+ 4 5    67   a a (a* + aa*b)*

14. How to convert a NFA-  into a FA

15. a b b - a,b a 3 2 41+

16. 1- ab  2345+ 

17. 1- a b  23+ 4 5    67   a a

18. Revision Understand Kleene’s Theorem Be able to convert Regular Expressions into NFA-  Be able to convert NFA-  into a Finite Automaton Read –Text Book Chapter 8