Honors Introduction to Computer Science Theory, 4003-389-01

Honors Introduction to Computer Science Theory, 4003-389-01, Fall 2011-12

Course Description

This course provides a challenging introduction to the theory of computation with an emphasis on problem solving. Topics include formal languages, grammars, automata theory, computability, and complexity.

Course Outcomes

Students will explain basic concepts in formal language theory, grammars, automata theory, computability theory, and complexity theory.
Students will relate practical problems to languages, automata, computability, and complexity.
Students will demonstrate an increased level of mathematical sophistication, including applying proof techniques to prove correctness of their solutions.
Students will describe and apply mathematical and formal techniques for solving problems in computer science.

Course Web Page

http://www.cs.rit.edu/~ib/Classes/CS389_Fall11/index.html

Instructor

Ivona Bezakova
bldg. GOL (70), room 3645
Email: my_initials at cs.rit.edu (please replace my_initials with ib)

Office hours:

Monday 10am-12pm
Tuesday 6-7pm (please come at 6pm or let me know that you are coming, otherwise I might leave),
Friday 12-1pm,
and, if none of the above times fits your schedule, by appointment.

Asking questions via email seems to work well for many people.

Lectures

Tuesday/Thursday, 4:00-5:50pm, classroom GOL-3560.

Required Book

Michael Sipser, Introduction to the Theory of Computation, (Second Edition), Thomson Course Technology, 2006 (or 2005).

Other Materials

Slides and information about reading and homework assignments, exams, etc.

Prerequisites

1016-366 (Discrete Mathematics II) or 1055-265 (Honors Discrete Mathematics) or permission of the instructor
Algorithms and data structures at the level of an introductory programming sequence.

Topic Outline

Regular languages and finite automata:
Strings and languages, Regular languages and regular expressions, Finite automata (DFA, NFA, NFA-Lambda), Languages accepted by finite automata, Transforming NFA-lambda to NFA, NFA to FA, Kleene's theorem, Pumping lemma, Minimal DFAs, Closure of regular languages under union, concat, intersection, complementation, Kleene star, Decision problems for regular languages and algorithms for these problems
Context-free languages:
Context-free grammars, Derivations, acceptance, Giving a grammar for a language / describing language generated by a grammar, Closure properties, Non-closure, Left-most derivations, parse/derivation trees, Ambiguity, CFLs and PDAs, PDAs are equivalent to CFGs, DPDAs are more powerful than FAs, PDAs are more powerful than DPDAs, Normal forms, CFL pumping lemma, CFL intersected with regular is CFL, decision problems for CFLs and their algorithms
Turing machines:
TM definition, Universal Turing machine, Languages accepted by TMs/ recognized by TMs, Recursive and recursively enumerable languages, RE intersect coRE = REC, Church-Turing thesis, Turing machine equivalences, Chomsky hierarchy
Computability:
Decision problems, Halting problem, Other undecidable problems
Complexity:
The class P / problems in P, The class NP / problems in NP / relation between P, NP, coNP, NP-completeness and reductions, SAT is NP-complete, Other NP-complete problems, Beyond NP

The Work

Homework Assignments

There are eight homework assignments, one per week except for the first week and the week of the midterm. Homeworks are due on Thursdays at 4pm, and are posted at least 6 days before they are due. The actual assignments will be available on the homeworks, reading, and slides page.

Unless it is specifically stated otherwise, you may work on and submit your homework in groups of 1 or 2. If you choose to work as a group of 2, both of you should contribute significantly to the solution for every question. You should submit only one copy of the homework with both your names on it. All authors have to be able to explain all solutions. Whether you submit on your own or with a partner, discussing homework with your fellow students is encouraged. However, after such discussions, all notes must be discarded, blackboards erased, and every group must write up their solutions in private without further consultations with your classmates or any written material other than your class notes, materials handed out in class, the textbook or this webpage. For every problem discussed with other students, state their names and briefly sketch the extent of your discussions (e.g. "solved together", or "clarified problem statement"). You are not allowed to look up the answers to your homeworks.

Your homework submissions must be submitted by Thursday, 4pm sharp. You have the following submission options:

Bring it to class, I will collect the homeworks at the start of the class.
Send it to me by e-mail, use the pdf-format. The e-mail must be sent before the beginning of the class.

I will not accept late assignments for any reason. I will drop the two lowest homework grades. However, a zero for cheating will not be dropped.

I will stop answering homework questions 24 hours before the homework is due. (This means that you can send an e-mail with a homework question by Wednesday 4pm and I will answer it as soon as possible, I will do my best to send my answer by 5pm.)

Midterm Exam

The midterm exam will take place on Thursday in week 6 (October 13th), in class. The exam will cover material from the first five weeks (specific book sections will be posted at the midterm website about about in week 5). The midterm is closed book and notes but you may bring one sheet of letter-sized paper with your own hand-written notes.

Final Exam

The final exam is semi-cumulative, meaning that it will focus on material from the second half of the quarter but it will also test high-level knowledge of the material from the first five weeks. It is closed book and notes but you may bring one sheet of letter-sized paper with your own hand-written notes, plus your midterm help-sheet.

Exams can not be made up except for real emergencies in which case proper documentation (like a doctor's note) will be required. If at all possible, you should contact me prior to the exam. Oversleeping, cars that don't start etc. do not constitute a valid excuse.

Evaluation

40% Homeworks and the best of
- 30% Midterm and 30% Final Exam or
- 25% Midterm and 35% Final Exam

Numerical grades will be converted to letter grades according to the following scale:
>90%: A; 80%-89%: B; 70%-79%: C; 60%-69%: D; <60%: F.
However, your final grade will never be more than one letter grade higher than the average of your midterm and final. In addition, if the average of your midterm and final is below 60%, you fail the course.

Tutoring

In addition to all of the usual support services RIT and the CS department offer, the CS theory faculty are offering their own tutoring service, featuring very qualified CS students. The tutoring takes place in the CS mentoring center (GOL-3660). For hours, see the theory tutoring page.

Disputing Your Grade

If you feel that an error was made in grading your homework or exam, you have one week from the moment the graded work was handed back to dispute your grade. All grading issues should be taken up with me; do not discuss grading issues with graders or tutors!
All grades will be posted on myCourses.

Academic Honesty

The DCS Policy on Academic Honesty will be enforced.
You should only submit work that is completely your own. Failure to do so counts as academic dishonesty and so does being the source of such work. Submitting work that is in large part not completely your own work is a flagrant violation of basic ethical behavior and will minimally be punished with failing the course.