1. Teori Bahasa dan Automata Lecture 6: Regular Expression
By:
Nur Uddin, Ph.D

2. Finite Automata

3. Finite Automata

4. Finite Automata

5. Formal Definition of Computation
Condition 1 says that the machine starts in the start state.
Condition 2 says that the machine goes from state to state according to the transition function.
Condition 3 says that the machine accepts its input if it ends up in an accept state.

6. Regular language

7. Example 1.13

8. Regular language

9. Designing Finite Automata
Done

10. Regular operations
We introduced and defined finite automata and regular languages.
Both help develop a toolbox of techniques for designing automata to recognize particular languages.
In arithmetic, the basic objects are numbers and the tools are operations for manipulating them, such as + and × .
In the theory of computation, the objects are languages and the tools include operations specifically designed for manipulating them. We define three operations on languages, called the regular operations, and use them to study properties of the regular languages.

11. Regular operations
The empty string ε is always a member of A*, no matter what A is.

12. Regular operations

13. Regular Expression

14. Regular Expression

15. Regular expression

16. Regular expression

17. Regular expression

18. Identity

19. Equivalence with finite automata
Regular expressions and finite automata are equivalent in their descriptive power.
This fact is surprising because finite automata and regular expressions superficially appear to be rather different.
However, any regular expression can be converted into a finite automaton that recognizes the language it describes, and vice versa.

20. Converting regular expression into NFA
Let’s convert R into an NFA N.

21. Converting regular expression into NFA
Let’s convert R into an NFA N.

22. Converting regular expression into NFA

23. Converting regular expression into NFA