skillsetfinal.pdf - CS 374 Algorithm and Models of...

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CS 374: Algorithm and Models of Computation (Spring 2017) Syllabus for Final Exam The final exam is cumulative and will test material covered in the entire course. However, a few topics will be omitted and they are highlighted below (basically we omit some advanced topics on regular languages and context free languages/grammars). Post midterm 2 skillset: Turing Machines and Complexity Classes Definition of a TM at a high-level and equivalence with programs. We will not ask you to design TMs for any concrete problem. Definition of decidable/recursive and recursively enumerable. Definition of P via TMs Knowledge of Universal TM and what it enables you to do - simulate a given TM on a given input. Undecidability Knowledge that the universal language and halting are undecidable. Ability to prove that problems on program behaviour are undecidable via reductions from L u and HALT . Rice’s theorem is not needed but it is useful to know what it says. You are free to use it. NP, NP-Completeness and Polynomial-time Reductions Definitions of NP, NP-Complete, NP-Hard Knowledge of standard NP-Complete problems: SAT, 3SAT, CircuitSAT, Indepensent Set, Clique, Vertex Cover, Hamiltonian Cycle/Path in directed/undirected graphs, 3Color, Color. Ability to prove that a given problem is in NP Ability to prove that a given problem is NP-Hard via a polynomial time reduction from an existing NP-Hard problem from the given list. Understand the definition of a polynomial-time reduction and its implications.
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