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Unformatted text preview: Computability & Complexity Theory Charles E. Hughes COT 6410 – Fall 2010 Notes 07/15/11 © UCF EECS 2 Who, What, Where and When • Instructor: Charles Hughes; Harris Engineering 247C; 8232762 (phone is not a good way to get me); [email protected] (email is a good way to get me) Subject: COT6410 • Web Page: http://www.cs.ucf.edu/courses/cot6410/fall2010 • Meetings: TR 6:00PM7:15PM, HEC118; 28 periods, each 75 minutes long. Final Exam is separate from class meetings • Office Hours: TR 3:30PM4:45PM 07/15/11 © UCF EECS 3 Text Material • This and other material linked from web site. • References: – Garey & Johnson, Computers and Intractability: A guide to the Theory of NPCompleteness , W. H. Freeman & Co., 1979. – Papadimitriou & Lewis, Elements of the Theory of Computation , PrenticeHall, 1997. – Hopcroft, Motwani&Ullman, Intro to Automata Theory, Languages and Computation 2nd Ed. , AddisonWesley, 2001. – Davis, Sigal and Weyuker, Computability, Complexity and Languages 2nd Ed. , Academic Press (Morgan Kaufmann), 1994. – Sipser, Introduction to the Theory of Computation 2nd Ed ., Course Technologies, 2005. Goals of Course • Introduce Computability and Complexity Theory, including – Simple notions in theory of computation • Algorithms and effective procedures • Decision and optimization problems • Yes versus no decision problems – Limits of computation • Turing Machines and other equivalent models • Determinism and nondeterminism • Undecidable problems • The technique of reducibility • The ubiquity of undecidability (Rice’s Theorem) • The notion of semidecidable (re) and of core sets – Complexity theory • Order notation (this should be a review) • Polynomial reducibility • Time complexity, the sets P, NP, coNP, NPcomplete, NPhard, etc., and the question does P=NP? Sets in NP and NPComplete. 07/15/11 © UCF EECS 4 07/15/11 © UCF EECS 5 Expected Outcomes • You will gain a solid understanding of various types of computational models and their relations to one another. • You will have a strong sense of the limits that are imposed by the very nature of computation, and the ubiquity of unsolvable problems throughout CS. • You will understand the notion of computational complexity and especially of the classes of problems known as P, NP, coNP, NPcomplete and NPHard. • You will (hopefully) come away with stronger formal proof skills and a better appreciation of the importance of discrete mathematics to all aspects of CS. 07/15/11 © UCF EECS 6 Keeping Up • I expect you to visit the course web site regularly (preferably daily) to see if changes have been made or material has been added....
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 Fall '10
 Dutton
 Computational complexity theory, Halting problem, UCF EECS

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