CSE 8813

THEORY OF COMPUTATION

Prof. Ioana Banicescu.

HOURS:

CLASS: Mon/Wed 3:30 - 4:45, Butler 103.

OFFICE: 320 Butler Hall, Mon/Wed 12:30 - 1:30; other times by appointment only. Email: ioana@cse.msstate.edu.

325-2756

TEXT BOOK - Recommended:

The Theory of Computation, Bernard M.Moret. Addison-Wesley, 1998.

Limits of Computation: An Introduction to the Undecidable and the Intractable, Edna E. Reiter and Clayton M. Johnson. CRC Press, 2013.

PREREQUISITES:

The required prerequisites are listed in the official university bulletin(CSE3813). Graduate level courses in algorithms and complexity of sequential and parallel algorithms are desirable.

OBJECTIVES:

The theoretical foundations of computer science have expanded substantially in recent years. The objective of this course is to introduce students to this fundamental area of computer science which enables students to focus on the study of abstract models of computation. These abstract models allow the students to assess via formal reasoning what could be achieved through computing when they are using it to solve problems in science and engineering. The course exposes students to the computability theory, as well as to the complexity theory. The goal is to allow them to answer fundamental questions about problems, such as whether they can or not be computed, and if they can, how efficiently.

The course introduces basic computation models and their properties, and the necessary mathematical techniques to prove more advanced attributes of these models. The students will be able to express computer science problems as mathematical statements and to formulate proofs. Upon completion of this course the students are expected to become proficient in key topics of theory of computation, and to have the opportunity to explore the current topics in this area.

COURSE REQUIREMENTS & GRADING POLICY:

During the semester, the students will take several test exams, a comprehensive final exam, give presentations, and/or write a research/term paper. The final grade will be based on all of the above (tests/quizzes/assignments: 30%; comprehensive final exam: 40%; class presentations:15%, and term papers: 15%).

COURSE OUTLINE:

The course will cover material from the following topics:

History and Preliminaries

Finite Automata and Regular Languages: determinism and nondeterminism, checking vs. computing, properties of finite automata, regular expressions, the pumping lemma, closure properties

Universal models of computations:issues of computability, the Turing machine, translation between models, model independence

Computability theory: primitive and partial recursive functions, encoding a turing machine, recursive and R.E. sets, Rice's theorem and the Recursion theorem, unsolvability

Complexity theory: reducibility among problems, reduction and complexity classes, hierarchy theorems, model-independent complexity classes, NP-completeness, space completeness, provably intractable problems

Proving problems hard: NP-complete problems, P-completeness proofs, Turing reductions and search problems, the polynomial hierarchy and enumeration problems

Complexity theory in practice: restriction of hard problems, strong NP-completeness, the complexity of approximation, the power of randomization

Average case complexity, models of parallel computation, communication and complexity, zero knowledge and probabilistically checkable proofs, complexity and constructive mathematics

ACADEMIC HONESTY, ETHICS IN RESEARCH AND SCHOLARLY ACTIVITIES:

Students are expected to familiarize themselves and follow the MSU Honor Code , as well as the CS department's policies on academic misconduct and on academic honesty with regard to homeworks, projects, exams, papers. These policies can be found on the MSU ethics in research and other scholarly activities and Mississippi State University policy regarding professional conduct pages respectively .

ATTENDANCE AND ADD/DROP POLICIES:

Attendance is required. Roll will be taken, and absences will be listed on midterm and final grade reports. Attendance may influence grades at border line. Makeup exams are allowed only in special circumstances where absences are certified by the Dean of Students office. At the beginning of the semester, students are encouraged to also review the Add/Drop policy.
Students who are auditing this course must attend at least 75% of the class lectures to avoid a grade of F.

[INSTRUCTOR] [HOURS] [PREREQUISITES] [OBJECTIVES] [REQUIREMENTS & GRADING] [OUTLINE]

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