Course Info
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Course Category
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Computer Science/Information Technology
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Course Level
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Graduate
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Credit Hours
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3
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Pre-requisites
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N/A
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Instructor
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Dr. Sarmad Abbasi
Ph.D Computer Science
Rutgers University, USA
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Course Contents
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Introduction to Theory of Computation and Overview of the Course,
Set Theory, Sets, Sequences, tuples, Functions, Relations and Graphs,
Turing Machine and Its Language,
Designing Turing Machines,
Variants of Turing Machines,
Enumerators, Dovetailing, The Church-Turing Thesis, Hilbert's tenth Problem,
Decidable Languages, The Acceptance Problem for DFAs,
The Halting Problem, Universal TM,
Undecidability of the Halting Problem,
Linear Bounded Automata, Computation Histories, Context Free Grammars,
Russell's Paradox, Reducibility, Emptiness Problem,
Post Correspondence Problem, Computable Functions,
Computable Functions, Reducibility,
Recursion Theorems, Logical Theories,
Godel's Theorem,
Oracles, Turing Reducibility,
A definition of information, Incompressible Strings,
Incompressible Strings, Complexity Theory,
Big Oh, Little Oh Notations, Time Complexity,
Non-Deterministic Time, The Class P, The Class NP,
Polynomial Time Verifiers,
Subset Sum Problem, Satisfiability,
NP-Completeness, 3-Color,
The Cook-Levin Theorem,
Independent Sets,
Clique, Vertex Cover,
Hamiltonian Path Problem,
The Subset Sum Problem,
The Traveling Salesman Problem,
An Approximation Algorithm for TSP,
Space Complexity,
Relationship between Space and Time Complexity, PSPACE-Completeness,
TQBF, Prove that TQBF is PSPACE-Complete,
FORMULA-GAME, Generalized Geography,
LOGSPACE Transducer,
Prove the Theorem: NL = co-NL
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