# CSI 4336: Introduction to Computation Theory, Fall 2010

## Objectives

This course is an introduction to the theory of computation. There are three main
parts to this course: the model of an abstract computer, *what* problems
can be computed, and *how efficiently* given problems can be computed.
This course forms the foundation for much of the subsequent work/research you
will do in computer science. One of the most fascinating parts of this topic is
that there are problems which we can describe simply (and we will) which have
not yet been solved.

The basic topics covered in this course are:

- formal models of computation
- regular languages, context free languages
- deterministic finite automata, non-deterministic finite automata
- Turing machines

- computability theory ("what sorts of problems can computers solve?")
- decidability
- reducibility

- complexity theory ("how efficiently can computers solve different problems?")
- time complexity, classes of complexity, P versus NP, NP-completeness
- space complexity
- intractability
- randomized classes of computation

**This is a difficult course.** Be prepared to invest the time
necessary to understand the concepts, and to do the assignments. My
best advice is to attend the lectures, ask questions, and start assignments early.

## Practical information

Lectures are from 11:00 AM to 12:15 PM in Rogers 104 on Tuesdays and Thursdays.

My office is in the Rogers Engineering and Computer Science building. My office hours are listed on my home page. I am glad to talk to students during and outside of office hours.

## Schedule

Here is a schedule of the material we will cover (order/content may be adjusted):

Week | Dates | Topics | Reading | Tuesday | Thursday |
---|---|---|---|---|---|

1 | Aug 23-27 | Introduction, discrete math foundations, proofs, languages | 0 | Hwk. 0 | |

2 | Aug 30-Sep 3 | Regular languages, finite automata, nondeterminism, regular expressions, equivalence of REs and FAs, closure properties for RLs, decision problems for RLs | 1.1-1.3, 4.1 (RL part) | Hwk. 1 | |

3 | Sep 6-10 | Nonregular languages, pumping lemma for RLs | 1.4 | Hwk. 2 | |

4 | Sep 13-17 | Context-free languages, push-down automata, normal forms for CFGs, ambiguity in CFGs, pumping lemma for CFLs, closure properties for CFLs, decision problems for CFLs | 2.1-2.3, 4.1 (CFL part) | Hwk. 3 | |

5 | Sep 20-24 | Exam 1 | |||

6 | Sep 27-Oct 1 | Turing machines, variants of the TM, nondeterministic TMs | 3 | Hwk. 4 | |

7 | Oct 4-8 | Universal machines, decidability, the halting problem, reducibility, undecidable problems by the dozen, Rice's theorem | 4.2, 5 | Hwk. 5 | |

8 | Oct 11-15 | Recursion theorem, fixed-point theorem, compressibility and descriptional complexity | 6.1, 6.4 | Hwk. 6 | |

9 | Oct 18-22 | Oracle computations, hierarchy of undecidability, logic and decidability, incompleteness | 6.2, 6.3 | Hwk. 7 | |

10 | Oct 25-29 | Exam 2 | |||

11 | Nov 1-5 | Computational complexity, models of computational efficiency, resource usage, complexity classes | 7.1 | ||

12 | Nov 8-12 | P and NP, polynomial-time reduction, TSP, Hamiltonian circuit and vertex cover | 7.2, 7.3 | Hwk. 8 | |

13 | Nov 15-19 | Boolean satisfiability, Cook-Levin theorem, NP-completeness, survey of NP-complete problems | 7.4, 7.5 | Hwk. 9 | |

14 | Nov 22-26 | More NP-Complete problems, co-NP, dealing with NP-completeness, space complexity and Savitch's theorem | 8.1-8.2, 8.4 | Thanksgiving break | |

15 | Nov 29-Dec 3 | Randomized polynomial time, probabilistic algorithms, primality | 10.1, 10.2, 10.4 | Hwk. 10 |

The final exam date will be Friday, December 10th at 2:00 PM. The latest university finals information is available here.

## Textbooks & resources

Required text: we will be using Michael Sipser's textbook Introduction to the Theory of Computation (2nd Edition). You can purchase this book from the bookstore or amazon, among other places.

Further online resources:

- We will use Blackboard only to keep track of course grades.
- Please see this STL cheatsheet (1) and this STL cheatsheet (2) for a quick overview of the STL.
- LaTeX information: LaTeX introduction, another LaTeX introduction, LaTeX reference
- Here is a C++ style guideline for the class. These also apply to Java.

## Grading

Grades will be assigned based on this breakdown:

- homework: 35%
- midterm exams: 40%
- final exam: 25%

A: 90-100, B+: 88-89, B: 80-87, C+: 78-79, C: 70-77, D: 60-69, F: 0-59

Some homeworks may be worth more than others. All exams are closed-book. The final will be comprehensive.

Homeworks should be written up in (nice-looking) LaTeX. Homeworks are due at the beginning of class on the due dates for full credit. Homeworks turned in after I have collected them but before the end of class will receive a 20% penalty. No homeworks will be accepted after class on the due date.

## Graduate credit

Students receiving graduate credit for this course will be required to complete additional components of several homework assignments. These components will give the advanced student an opportunity to explore topics, to implement algorithms, and to apply techniques that are not normally covered by undergraduates in this course. Scores on these additional components will be included in the homework assignment portion of the grade. Students receiving graduate credit will also have additional exam questions on these advanced topics, and the scores for these extra questions will be included in the examination portion of the grade. The set of topics for graduate credit include:

- the recursion and fixed-point theorems
- Kolmogorov complexity
- hierarchy of undecidability
- logic, decidability, and incompleteness
- space complexity
- randomized complexity classes

## Policies

- Check this website every day for updates and announcements. We only meet three times a week, but I may post updates at any time. It is your responsibility to follow these updates by reading this website.
**All work in this course is strictly individual, unless the instructor explicitly states otherwise.**While discussion of course material is encouraged, collaboration on any work for the course is not allowed. Collaboration includes (but is not limited to) discussing with anyone other than the professor any material that is specific to completing an assignment. You are*not*to work with anyone else on any assignment unless I expressly permit it. You*are*encouraged to discuss the course material with the professor, preferably in office hours, and also by email.- Baylor policy requires 75% class attendance from each student. Even "excused" absences are included in the overall absent count. If a student attends less than 75% of the classes, he or she will automatically fail the course.
- In order to facilitate keeping attendance, on the second class meeting I will ask you to choose a seat for the rest of the course. Please sit in your chosen seat for the remainder of the course.
- Homeworks which are late are not accepted. Exams are the only things which may be made up with prior arrangement (made at least one class before to the exam) or due to illness, with a note from a health care professional.
- Bring any grading correction requests to my attention within 2 weeks of receiving the grade or before the end of the semester, whichever comes first. After that, I will not adjust your grade. If you find any mistake in grading, please let me know.

## Academic honesty

I take academic honesty very seriously.

Many studies, including one by Sheilah Maramark and Mindi Barth Maline have suggested that "some students cheat because of ignorance, uncertainty, or confusion regarding what behaviors constitute dishonesty" (Maramark and Maline, Issues in Education: Academic Dishonesty Among College Students, U.S. Department of Education, Office of Research, August 1993, page 5). In an effort to reduce misunderstandings in this course, a minimal list of activities that will be considered cheating have been listed below.

- Copying another student's work. Simply looking over someone else's source code is copying.
- Providing your work for another student to copy.
- Collaboration on any assignment, unless the work is explicitly given as collaborative work.
- Using notes or books during any exam.
- Giving another student answers during an exam.
- Reviewing a stolen copy of an exam.
- Plagiarism.
- Studying tests or using assignments from previous semesters.
- Providing someone with tests or assignments from previous semesters.
- Taking an exam for someone else.
- Turning in someone else's work as your own work.
- Studying a copy of an exam prior to taking a make-up exam.
- Providing a copy of an exam to someone who is going to take a make-up exam.
- Giving test questions to students in another class.
- Reviewing previous copies of the instructor's tests without permission from the instructor.

Copyright © 2007 Greg Hamerly, with some content
taken from a syllabus by Jeff Donahoo.

Computer Science Department

Baylor University