4 peres asher quantum theory concepts and methods new

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4. Peres, Asher. Quantum Theory: Concepts and Methods.New York, NY: Springer, 1993. ISBN: 9780792325499.
CS4029 TOPICS IN THEORY OF COMPUTATIONPre-requisite: CS3001 Theory of ComputationELECTIVELTPC4004Total Hours: 56 Hrs Module 1 (14 Hours)Recursion, The primitive recursive functions, Turing machines, Arithmetization, Coding functions ,The normal form theorem, The basic equivalence and Church’s thesis, Canonical coding of finite sets,Computable and computably enumerable sets, Diagonalization, Computably enumerable sets ,Undecidable sets , Uniformity, Many-one reducibility, The recursion theorem, Proof for Godel’sIncompleteness Theorem based on Recursion theorem.Module 2 (14 Hours)The arithmetical hierarchy, Computing levels in the arithmetical hierarchy , Relativized computationand Turing degrees, Turing reducibility , Limit computable sets, Incomparable degrees Module 3 (14 Hours)The priority method, Diagonalization, Turing incomparable sets , Undecidability , Constructivism,randomness and Kolmogorov complexity, Compressibility and randomness, UndecidabilityModule 4 (14 Hours)Scheme, programming and computability theory based on a term-rewriting, "substitution" model ofcomputation by Scheme programs with side-effects; computation as algebraic manipulation: Schemeevaluation as algebraic manipulation and term rewriting theory.References:1. R. I. Soare, Recursively enumerable sets and degrees, Springer-Verlag, 19872. G. E. Sacks, Higher recursion theory, Springer Verlag, 1990.3. M. Li and P. Vitányi, An introduction to Kolmogorov complexity and its applications, Springer-Verlag, 19934. Dexter C. Kozen, Automata and Computability, Springer-Verlag, Inc., New York, NY, 1997.5. S. C. Kleene, Introduction to Metamathematics, Van Nostrand Co., Inc., Princeton, New Jersey, 1950.6. MIT OpenCourseWare on Computability Theory of and with Scheme at -engineering-and-computer-science/6-844-computability-theory-of-and-with-scheme-spring-2003/accessedon26/11/2010
CS4030 COMPUTATIONAL COMPLEXITYPre-requisite: NilELECTIVELTPC4004Course Outcomes:CO1: Place a given computational problem to the appropriate complexity classCO2: Establish connections between problems using reductionsCO3: Prove completeness of a given problem with respect to a given complexity classCO4: Prove hardness of approximation using gap reductionsTotal Hours: 56 Hrs Module 1 (14 Hours)Review of Complexity Classes, NP and NP Completeness, Space Complexity, Hierarchies, Circuit sat-isfiability, Savitch and Immerman theorems, Karp Lipton Theorem.Module 2 (14 Hours)Randomized Complexity classes, Adleman's theorem, Sipser Gacs theorem, Randomized Reductions,Counting Complexity, Permanent’s and Valiant’s TheoremModule 3 (14 Hours)Parallel complexity, P-completeness, Sup-liner space classes, Renegold's theorem, Polynomialhierarchy and Toda's theoremModule 4 (14 Hours)Arthur Merlin games, Graph Isomorphism problem, Goldwasser-Sipser theorem, Interactive Proofs,Shamir's theorem.

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