1. 1 CSCI-2400 Models of Computation

2. 2 Computation CPU memory

3. 3 CPU input memory output memory Program memory temporary memory

4. 4 CPU input memory output memory Program memory temporary memory compute Example:

5. 5 CPU input memory output memory Program memory temporary memory compute

6. 6 CPU input memory output memory Program memory temporary memory compute

7. 7 CPU input memory output memory Program memory temporary memory compute

8. 8 Automaton CPU input memory output memory Program memory temporary memory Automaton

9. 9 Different Kinds of Automata Automata are distinguished by the temporary memory Finite Automata: no temporary memory Pushdown Automata: stack Turing Machines: random access memory

10. 10 input memory output memory temporary memory Finite Automaton Finite Automaton Example: Vending Machines (small computing power)

11. 11 input memory output memory Stack Pushdown Automaton Pushdown Automaton Example: Compilers for Programming Languages (medium computing power) Push, Pop

12. 12 input memory output memory Random Access Memory Turing Machine Turing Machine Examples: Any Algorithm (highest computing power)

13. 13 Finite Automata Pushdown Automata Turing Machine Power of Automata Less powerMore power Solve more computational problems

14. 14 Languages

15. 15 A language is a set of strings String: A sequence of letters Examples: “cat”, “dog”, “house”, … Defined over an alphabet:

16. 16 Alphabets and Strings We will use small alphabets: Strings

17. 17 String Operations Concatenation

18. 18 Reverse

19. 19 String Length Length: Examples:

20. 20 Length of Concatenation Example:

21. 21 Empty String A string with no letters: Observations:

22. 22 Substring Substring of string: a subsequence of consecutive characters String Substring

23. 23 Prefix and Suffix Prefixes Suffixes prefix suffix

24. 24 Another Operation Example: Definition:

25. 25 The * Operation : the set of all possible strings from alphabet

26. 26 The + Operation : the set of all possible strings from alphabet except

27. 27 Languages A language is any subset of Example: Languages:

28. 28 Note that: Sets Set size String length

29. 29 Another Example An infinite language

30. 30 Operations on Languages The usual set operations Complement:

31. 31 Reverse Definition: Examples:

32. 32 Concatenation Definition: Example:

33. 33 Another Operation Definition: Special case:

34. 34 More Examples

35. 35 Star-Closure (Kleene *) Definition: Example:

36. 36 Positive Closure Definition: