1. Theory of Languages and Automata
By: Mojtaba Khezrian

2. Review Alphabetic ……. {0,1} String ….. x=‘101010’
Length of String ….. |x|
Language
Union
Intersection
Concat

3. Review

4. G =(V,T,P,S) V= nonFinal symbol T= Alphabetic P= Rules
Grammar
G =(V,T,P,S)
V= nonFinal symbol
T= Alphabetic
P= Rules
S= Starting symbol

5. Language of Grammar

6. Language of Grammar

7. Language of Grammar

8. Language of Grammar

9. How to Write Grammar?
First split the language to small parts then write the grammar of them. Finally join all of them.

10. 1: Split like: A A A …. A A is the symbol of even length
How to Write Grammar?
1: Split like: A A A …. A A is the symbol of even length

11. How to Write Grammar?
2: Split like: X A A is the symbol of even length X is the symbol of aa or ab or bb or ba

12. How to Write Grammar?
3: Split like: A B A,B is the symbol of even length

13. How to Write Grammar?
4: Split like: A X A is the symbol of even length X is the symbol of aa or ab or bb or ba

14. How to Write Grammar?
Split like: X A A is the symbol of even length X is the symbol of a or b

15. How to Write Grammar?
1: Split like: b…a and a…b

16. How to Write Grammar?
2: Split like: b…a… and a…b…

17. How to Write Grammar?
3: Split like: AB

18. How to Write Grammar?
3: Split it to two languages: L1 and L2 L1: n,m are even L2: n,m are odd

19. How to Write Grammar?

20. Type of Grammar Type-3 Grammar (Regular Grammar)
Type-2 Grammar (Context free Grammar)
Type-1 Grammar (Context Sensitive Grammar)
Type-0 Grammar

21. Type-3 Grammar (Regular Grammar)
If it would be right-linear:
Or left-linear:

22. Type-3 Grammar (Regular Grammar)

23. Type-2 Grammar (Context Free Grammar)

24. Type-1 Grammar (Context Sensetive Grammar)

25. Type-1 Grammar (Context Sensitive Grammar)

26. Type-0 Grammar

27. Type-0 Grammar

28. Type of Language Type-3 Language (Regular Language)
Type-2 Language (Context Free Language)
Type-1 Language (Context Sensitive Language)
Type-0 Language

29. Type of Language Type-3 If there is a type-3 grammar for it
Type-2 If there is a type-2 grammar and no type-3 grammar for it
Type-1 If there is a type-1 grammar and no type-3 and type-2 grammar for it
Type-0 If there is a type-0 grammar and no type-3 and type-2 and type-1 grammar for it

30. Type of Language

31. Type of Automata Automata for type-3 language (Finite Automata)
Automata for type-2 language (Push-down Automata)
Automata for type-1 language (Linear Bounded Automata)
Automata for type-0 language (Turing Machine)

32. Type of Automata

33. Finite Machine

34. Finite Machine
Accept: If at the end of string, machine is stated in one of final states.
Reject: If at the end of string, machine is stated in one of non-final states or before end of string it’ll be stoped.

35. Finite Machine

36. Finite Machine

37. Example

38. Language of a Finite machine
If A is the set of all strings that machine M accepts, we say that A is the language of machine M and write: L(M) = A.
M recognizes A
M accepts A.

39. Finite Machine

40. Finite Machine

41. Finite Machine

42. Example