COT6410NotesFall2010 - Computability &...

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Unformatted text preview: Computability & Complexity Theory Charles E. Hughes COT 6410 Fall 2010 Notes 11/16/10 UCF EECS 2 Who, What, Where and When Instructor: Charles Hughes; Harris Engineering 247C; 823-2762 (phone is not a good way to get me); charles.e.hughes@knights.ucf.edu (e-mail is a good way to get me) Subject: COT6410 Web Page: http://www.cs.ucf.edu/courses/cot6410/fall2010 Meetings: TR 6:00PM-7:15PM, HEC-118; 28 periods, each 75 minutes long. Final Exam is separate from class meetings Office Hours: TR 3:30PM-4:45PM 11/16/10 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 NP-Completeness , W. H. Freeman & Co., 1979. Papadimitriou & Lewis, Elements of the Theory of Computation , Prentice-Hall, 1997. Hopcroft, Motwani&Ullman, Intro to Automata Theory, Languages and Computation 2nd Ed. , Addison-Wesley, 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 non-determinism Undecidable problems The technique of reducibility The ubiquity of undecidability (Rices Theorem) The notion of semi-decidable (re) and of co-re sets Complexity theory Order notation (this should be a review) Polynomial reducibility Time complexity, the sets P, NP, co-NP, NP-complete, NP-hard, etc., and the question does P=NP? Sets in NP and NP-Complete. 11/16/10 UCF EECS 4 11/16/10 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, co-NP, NP-complete and NP-Hard. 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. 11/16/10 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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COT6410NotesFall2010 - Computability &...

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