Spring 2010

Mathematical Foundations of Computer Science

Welcome to CS46: Theory of Computation! Computer technology changes rapidly, but the underlying model of computation is relatively unchanged in the past 50 years. How do computers compute, and why is this method of computation preferred over others methods. Do other methods even exist? Could we solve more interesting problems with another model? Could we solve the same problems we solve today using a simpler model of computation? In this course will will look at various theoretical models of computation and examine the computational power of these models. For each model we consider problems that can and cannot be solved, and develop a rigorous method of classifying how difficult certain problems are to compute. While the course emphasis is on theory, there are many applications of the topics discussed. Regular expressions, compilers, CPU job scheduling, and many other real-world problems have some underlying computational model rooted in the theory of computation.

- Final Exam is May 6th, 9am-Noon

WEEK |
DAY |
ANNOUNCEMENTS |
TOPIC & READING |
HOMEWORK |

1 | Jan 19 | Math preliminaries p1-28 Languages p42-51 |
HW 1 | |

Jan 21 | ||||

2 | Jan 26 | Finite automata p55-89,102-109 regular languages Context free grammars p113-122 |
HW 2 | |

Jan 28 | Drop/Add ends (Jan 29) |
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3 | Feb 02 | HW 3 | ||

Feb 04 | ||||

4 | Feb 09 | Pushdown automata Context free languages Determistic CFLs p123-149 |
HW 4 | |

Feb 11 | ||||

5 | Feb 16 | HW 5 | ||

Feb 18 | ||||

6 | Feb 23 | Deterministic CFLs | HW 6 | |

Feb 25 | Turing Machine Intro | |||

7 | Mar 02 | Turing machine computation |
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Mar 04 | ||||

Mar 09 |
Spring Vacation |
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Mar 11 |
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8 | Mar 16 | Turing machine extensions | ||

Mar 18 | ||||

9 | Mar 23 | Non-determinism and Turing Machines |
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Mar 25 | Last day to declare CR/NC or withdraw with a "W" (Mar 26) |
Unsolvable problems | HW 7 | |

10 | Mar 30 | |||

Apr 01 | ||||

11 | Apr 06 | Computational complexity | HW 8 | |

Apr 08 | ||||

12 | Apr 13 |
No Class |
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Apr 15 | NP-complete problems | |||

13 | Apr 20 | Complexity hierarchies Wrapup |
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Apr 22 | ||||

14 | Apr 27 | |||

Apr 29 | ||||

May 06 |
Final exams start |
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May 15 |
Final exams end |

40% | Homework assignments |

10% | Lab assignments |

10% | Class Participation and Discussion |

20% | Midterm exam |

20% | Final Exam |

Each week, reading and several problems will be assigned. You should work on all of the problems but hand in clearly written solutions to a subset (usually four) of the problems at the beginning of the Thursday session. Sometimes I will specify certain problems that must be part of what you hand in. All students should be prepared to discuss the reading and solutions to any of the problems. Always do all parts of a problem unless I specify otherwise.

It is best if you start the assignments early, and at least read the problems and make sure you understand what the problem is asking soon after the problems are assigned. If you do not understand a problem, ask for clarification. I often find that the solution to problems in this course only come if the problems sit in your brain for several hours, even if you are not constantly thinking about the problem during that time.

Late assignments will not be accepted except in extreme situations and only if you contact me well before the deadline. Even if you do not fully complete an assignment, you may submit what you have done to receive partial credit.

Contact Tracey Rush at the Dean's office and follow these steps for obtaining accommodations.

Academic honesty is required in all work you submit to be graded. You may not submit work done with (or by) someone else. You may not examine or use work done by others to complete your own work. You may discuss assignment specifications and requirements with others in the class to be sure you understand the problem. In addition, you are allowed to work with others to help learn the course material. However, with the exception of the student mentors and your partner on group assignments, you may not work with others on your assignments.

All code you submit must be your own with the following permissible exceptions: code distributed in class, code found in the course text book, and code worked on with an partner. In these cases, you should always include detailed comments that indicates on which parts of the assignment you received help, and what your sources were.

"It is the opinion of the faculty that for an intentional first offense, failure in the course normally is appropriate. Suspension for a semester or deprivation of the degree in that year may also be appropriate when warranted by the seriousness of the offense." - Student Handbook (2009-2010, pg18 Section I.B.3.b.i)

Please see me if there are any questions about what is permissible.

A real DIY Turing Machine

JFLAP: Java Formal Languages and Automata
Package