In the name of ALLAH, the most beneficient, the most merciful

# Theory of Computation (CS701)

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## Course Contents

Introduction, Set Thoery, Sequences, Tuples, Functions, Relations, Graphs, Turing Machines, Enumerators, Dovetailing, The Church-Turing Thesis, Hilbert 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 Paradox, Emptiness Problem, Post Correspondence Problem, Computable Functions, Reducibility, Recursion Theorem, Logical Theories, Godels Theorem, Oracles, Turing Reducibility, A definition of Information, Incompressible Strings, Complexity Theory, Big Oh and Little Oh Notations, Time Complexity, Non-Deterministic Time, The Class P, The Class NP, Polynomial Time Verifiers, Subset Sum Problem, Satisfiability, NP-Completness, 3-Color Problem, The Cook-Levin 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, 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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