- 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.

bldg. 70, room 3645

Email: my_initials at cs.rit.edu (please replace my_initials with ib)

- Monday 10-12pm,
- Thursday 3-3:45pm,
- Friday 3-4pm,
- and by appointment.

- 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.

**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

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
**Tuesday, 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 stop answering homework questions at 8pm on Mondays. (This means that you can send an e-mail with a homework question by Monday 8pm and I will answer it as soon as possible, I will do my best to send my answer by 10pm.)

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.

- 50% Homeworks and the best of
- 25% Midterm and 25% Final Exam or
- 20% Midterm and 30% Final Exam

>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.

All grades will be posted on myCourses.

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.