CS 5000
Computability Theory

Course Description

Rigorous introduction to fundamental concepts of finite automata and computability. Topics include, but are not limited to:

• Finite-State Automata and Regular Languages;
• Context-Free Languages and Stack Machines;
• Foundations of Computability;
• Turing Machines;
• Propositional Calculus.

Objectives

• To enable the students to understand the basics of finite state automata, differences between determinism and non-determinism, closure properties, correspondences between languages and computational devices, and fundamental decision procedures;
• To enable students to construct, use, and reason about the automata for processing regular and context-free languages;
• To enable students to tell when a language is not regular;
• To familiarize students with the basics of computability theory (recursion theory);
• To enable students to understand, compare, and reason about two fundamental models of computation: the Turing Machine and the Partially Computable Function;
• To familiarize students with propositional calculus and resolution.

Text Books

We will use "Computability, Complexity, and Languages" by Davis, Sigal, and Weyuker.

There are a few other textbooks that are worth reading. Examples, proofs, and explanations from these books will be used in the lectures throughout the semester.

• John Hopcroft and Jeffery Ullman. "Introduction to Automata Theory, Languages, and Computation."
• Elaine Rich. "Automata, Computability, and Complexity."
• Adam Brooks Webber. "Formal Language: A practical Introduction."
• John Carroll and Darrell Long. "Theory of Finite Automata."

Assignments

There will be regular assignments throughout the semester. Most assignments will be pencil and paper. If there are multiple sheets in the assignment you submit, they should be enumerated and stapled. No late submissions will be accepted.

Please be cognizant of deadlines and due dates. Your grades will be periodically posted on the Eagle server. If you do not have an account on that server, go to the above link and follow the instructions on how to get a new account. You have to have a valid cc.usu.edu e-mail address before you can get an account on Eagle.

You must be registered for the class in order to submit your assignments, have them graded, and take exams. If you are not registered, the grader will not grade your homework submissions. If the grader grades your homework by mistake, you will receive no credit for your work.

Grading

• Homework - 20 percent;
• Midterm - 30 percent;
• Final - 50 percent.

Plagiarism

You are free to talk with each other about regular assignments in general terms. However, you must write your own solutions and/or computer code. No collaboration is allowed on exams.

Activities that violate the plagiarism policy include (but are not limited to): copying another person's work on a programming project, homework assignment, or exam; using any reference not authorized by the instructor on a programming project, homework assignment, or exam.

The penalty for violating the plagiarism policy may be an F in the course. Appropriate university authorities may be informed of cheating incidents in a formal letter.

ADA Compliance

If a student has a disability that will likely require some accomodation by the instructor, the student must contact the instructor and document the disability through the Disability Resource Center, preferably during the first week of the course. Any request for special considerations relating to attendance, pedagogy, taking of examinations, etc. must be discussed with and approved by the instructor. In cooperation with the Disability Resource Center, course materials can be provided in alternative formats, e.g., large print, audio, diskette, or Braille.

Incompletes

The University policy will be adhered to for incompletes. This means that an incomplete cannot be given to prevent receipt of a bad grade. Under no circumstances can an incomplete be given for which a re-take of the class is required to make up the work. In such situations, a withdrawal or late withdrawal is required. If a student feels that an incomplete is appropriate, it is their responsibility to immediately discuss the matter with their instructor.

Contact

My office is in 401E, Old Main. My office hours for this class are from 5:00pm to 6:00pm on Wednesday or by apppointment.My e-mail is vladimir.kulyukin@usu.edu.