2. 1 Theory of Computation 計算理論

3. 2 Instructor: 顏嗣鈞 E-mail: yen@ee.ntu.edu.tw Web: http://www.ee.ntu.edu.tw/~yen Time: 9:10-12:10 PM, Monday Place: BL 103 Office hours: by appointment Class web page: http://www.ee.ntu.edu.tw/~yen/courses/TOC-2008.htm

4. 3 Automata, Computability and Complexity: Theory and Applications by Elaine A. Rich Publisher: Pearson Pub. Date: October 2007 ISBN-13: 9780132288064 Textbook

5. 4 : Introduction to Automata Theory, Languages, and Computation John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman, (2nd Ed. Addison-Wesley, 2001) Reference

6. 5 1st Edition Introduction to Automata Theory, Languages, and Computation John E. Hopcroft, Jeffrey D. Ullman, (Addison-Wesley, 1979)

7. 6 3rd Edition : Introduction to Automata Theory, Languages, and Computation John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman, (Addison-Wesley, 2006)

8. 7 Grading HW/Project : 20% Midterm exam.: 40% Final exam.: 40%

9. 8 Why Study Automata Theory? Finite automata are a useful model for important kinds of hardware and software: Software for designing and checking digital circuits. Lexical analyzer of compilers. Finding words and patterns in large bodies of text, e.g. in web pages. Verification of systems with finite number of states, e.g. communication protocols.

10. 9 Why Study Automata Theory? (2) The study of Finite Automata and Formal Languages are intimately connected. Methods for specifying formal languages are very important in many areas of CS, e.g.: Context Free Grammars are very useful when designing software that processes data with recursive structure, like the parser in a compiler. Regular Expressions are very useful for specifying lexical aspects of programming languages and search patterns.

11. 10 Why Study Automata Theory? (3) Automata are essential for the study of the limits of computation. Two issues: What can a computer do at all? (Decidability) What can a computer do efficiently? (Intractability)

12. 11 Applications Theoretical Computer Science Automata Theory, Formal Languages, Computability, Complexity … Compiler Prog. languages Comm. protocols circuits Pattern recognition Supervisory control Quantum computing Computer-AidedVerification...

13. 12 Aims of the Course To familiarize you with key Computer Science concepts in central areas like - Automata Theory - Formal Languages - Models of Computation - Complexity Theory To equip you with tools with wide applicability in the fields of CS and EE, e.g. for - Complier Construction - Text Processing - XML

14. 13 Fundamental Theme What are the capabilities and limitations of computers and computer programs? –What can we do with computers/programs? –Are there things we cannot do with computers/programs?

15. 14 Studying the Theme How do we prove something CAN be done by SOME program? How do we prove something CANNOT be done by ANY program?

16. 15 Example: The Halting Problem (1) Consider the following program. Does it terminate for all values of n  1? while (n > 1) { if even(n) { n = n / 2; } else { n = n * 3 + 1; }

17. 16 Example: The Halting Problem (2) Not as easy to answer as it might first seem. Say we start with n = 7, for example: 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 In fact, for all numbers that have been tried (a lot!), it does terminate...... but in general?

18. 17 Example: The Halting Problem (3) Then the following important undecidability result should perhaps not come as a total surprise: It is impossible to write a program that decides if another, arbitrary, program terminates (halts) or not. What might be surprising is that it is possible to prove such a result. This was first done by the British mathematician Alan Turing.

19. 18 Our focus Automata Computability Complexity

20. 19 Topics 1. Finite automata, Regular languages, Regular grammars: deterministic vs. nondeterministic, one-way vs. two-way finite automata, minimization, pumping lemma for regular sets, closure properties. 2. Pushdown automata, Context-free languages, Context-free grammars: deterministic vs. nondeterministic, one-way vs. two-way PDAs, reversal bounded PDAs, linear grammars, counter machines, pumping lemma for CFLs, Chomsky normal form, Greibach normal form, closure properties. 3.

21. 20 Topics (cont’d) 3. Linear bounded automata, Context- sensitive languages, Context-sensitive grammars. 4. Turing machines, Recursively enumerable sets, Type 0 grammars: variants of Turing machines, halting problem, undecidability, Post correspondence problem, valid and invalid computations of TMs.

22. 21 Topics (cont’d) 5. Basic recursive function theory 6. Basic complexity theory: Various resource bounded complexity classes, including NLOGSPACE, P, NP, PSPACE, EXPTIME, and many more. reducibility, completeness. 7. Advanced topics: Tree Automata, quantum automata, probabilistic automata, interactive proof systems, oracle computations, cryptography.

23. 22 Who should take this course? YOU

24. 23 Languages The terms language and word are used in a strict technical sense in this course: A language is a set of words. A word is a sequence (or string) of symbols.  (or ) denotes the empty word, the sequence of zero symbols.

25. 24 Symbols and Alphabets What is a symbol, then? Anything, but it has to come from an alphabet which is a finite set. A common (and important) instance is  = {0, 1}. , the empty word, is never an symbol of an alphabet.

26. 25 Computation CPU memory

27. 26 CPU input memory output memory Program memory temporary memory

28. 27 CPU input memory output memory Program memory temporary memory compute Example:

29. 28 CPU input memory output memory Program memory temporary memory compute

30. 29 CPU input memory output memory Program memory temporary memory compute

31. 30 CPU input memory output memory Program memory temporary memory compute

32. 31 Automaton CPU input memory output memory Program memory temporary memory Automaton

33. 32 Different Kinds of Automata Automata are distinguished by the temporary memory Finite Automata: no temporary memory Pushdown Automata: stack Turing Machines: random access memory

34. 33 input memory output memory temporary memory Finite Automaton Finite Automaton Example: Vending Machines (small computing power)

35. 34 input memory output memory Stack Pushdown Automaton Pushdown Automaton Example: Compilers for Programming Languages (medium computing power) Push, Pop

36. 35 input memory output memory Random Access Memory Turing Machine Turing Machine Examples: Any Algorithm (highest computing power)

37. 36 Finite Automata Pushdown Automata Turing Machine Power of Automata Less powerMore power Solve more computational problems