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CS 6382.001.19S (Spring'2019) Theory of Computation

1:00-2:15pm TuTh, ECSN 2.112

This course consists of five parts:

Theory of Deterministric Computation

Theory of Nondeterministic Computation

Theory of Parallel Computation

Theory of Probabilistic Computation

Theory of Approximate Computation

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Contact Information of Professor

Office Hours: Thuesday 4:00 - 5:00PM

in Room ECSS 3-611.

homepage: http://www.utdallas.edu/~dxd056000

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Teaching Assistants:

Please click here for information on TA
Shuyang Gu

Office Hours: 10:00am-12:00pm on Tuesday and Thursday

in ECSS 2.103B1

Email: [email protected]

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Reference Books

Ding-Zhu Du and Ker-I Ko:

Theory of Computational Complexity (2nd ed.)

John-Wiley

ISBN-13: 978-1118306086

Published: June 2014

Errata

Review

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Lectures

(* means 'sketch')
Unit I (Theory of Deterministic Computation)

Lecture 1-1 Turing Machine (Sec. 1.1-2)

Lecture 1-2 Time and Space of DTM (Sec.1.2)

Lecture 1-3 Undecibality (Sec. 1.5-6)

* Lecture 1-4 Recursive Function

Lecture 1-5 Hierarchy Theorem

Unit II (Theory of Nondeterministic Computation}

Lecture 2-1 Time and Space of NTM
(Sec.1.3-4)

Lecture 2-2 NP class (Sec. 2.1)

Lecture 2-3 Cook Theorem (Sec. 2.2)

Lecture 2-4 Proof of NP-hardness
(Sec.
2.3-4)

Read Me Logic Puzzle

Lecture 2-5 Polynomial-time
Hierachy (Sec. 3.1-2)

Lecture 2-6 Complete Problem
in HP (Sec. 3.3)

* Lecture 2-7 Characterization of
PSPACE (Sec. 3.4)

Lecture 2-8 PSPACE-complete (Sec.3.5)

Read Me GO is PSPACE-hard

Unit III (Theory of Parallel Computation)

Lecture 3-1 P-size Circuit (Sec. 6.1-2)

Lecture 3-2 NC Class (Sec. 6.5)

* Lecture 3-3 Separating NC Hierachy (Sec.
6.6, 6.4)

Lecture 3-4 P-complete (Sec, 6.7)

Unit IV (Theory of Probablistic Computation)

* Lecture 4-1 Random Algorithm (Sec. 8.1)

* Lecture 4-2 Probabilistic TM (Sec.
8.2-6)

Lecture 4-3 Counting Class #P (Sec.
9.1-2)

Lecture 4-4 #P-complete (Sec. 9.2)

Read Me Influence Spread is #P-hard

Unit V (Theory of Approximate Computation)

Lecture 5-1 Approximations for NP-hard
Problems (Sec. 2.5)

* Lecture 5-2 Reduction with
Gap (Sec. 2.5)

Lecture 5-3 APX-complete (Sec. 11.5)

* Lecture 5-4 PCP Theorems

Lecture 5-5 Set-Cover and Indepedent
Set (Sec. 11.5)

Final Exam

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Homeworks and Examinations

There are 4 homeworks which will be given in Elearning.

There are two exams: Midterm and Final Exam. Schedules
will be anounced in Elearning.

Homeworks have totally 40 points,
two exams have totally 60 points.

Grades will be assigned according to the total number
of received points:

A >= 85 > B >= 70 > C >= 50.