Course Info

Course Category

Computer Science/Information Technology

Course Level

Graduate

Credit Hours

3

Prerequisites

N/A

Instructor

Dr. Sarmad Abbasi Ph.D Computer Science Rutgers University, USA


Course Contents

Introduction, Set Thoery, Sequences, Tuples, Functions, Relations, Graphs, Turing Machines, Enumerators, Dovetailing, The ChurchTuring Thesis, Hilbert's Tenth Problem, Decidable Languages, The Acceptance Problem for DFAs, The Halting Problem, Universal TM, Undicidability of the Halting Problem, Linear Bounded Automata, Computation Histories, Context Free Grammars, Russell's Paradox, Emptiness Problem, Post Correspondence Problem, Computable Functions, Reducibility, Recursion Theorem, Logical Theories, Godel's Theorem, Oracles, Turing Reducibility, A definition of Information, Incompressible Strings, Complexity Theory, Big Oh and Little Oh Notations, Time Complexity, NonDeterministic Time, The Class P, The Class NP, Polynomial Time Verifiers, Subset Sum Problem, Satisfiability, NPCompletness, 3Color Problem, The CookLevin Theorem, Independent Sets Problem, Clique, Vertex Cover, Hamiltonian Path Problem, The Subset Sum Problem, The Traveling Salesman Problem, Space Complexity, Relationship between Space and Time Complexity, PSPACECompleteness, TQBF, Prove that TQBF is PSPACEComplete, FORMULAGAME, Generalized Geography, LOGSPACE Transducer, Prove the Theorem: NL = coNL.


