Theory of computation: TOPICS

  • Theory of computation:

    • automata and formal languages

    • computability (recursion) theory

TC computability theory studies

  • computable functions

  • Turing degrees

  • generalized computability and definability

  • overlaps with proof theory and effective descriptive set theory

TC Concepts

  • models of computation

  • effective computation

  • Entscheidungsproblem (the decision problem)

  • Functions computable function primitive recursive function recursive function total function

  • Theory of computation: Introduction background definitions on strings and numbers automata and formal languages computability (recursion) theory overview of computability

  • Post machines Formal systems and r.e. sets An alternative view of formal systems Formal systems and functions Goals and recursion Gödel numbering The universal machine The halting problem. Representability. Diagonalisation. Gödel's first incompleteness theorem. Turing Machines. Post systems.

  • Register machines Register machines. Primitive recursion. Pairing and tupling functions. Primitive register machines. Diagonalisation for primitive register machines and general recursive functions. Gödel-numbering for register machines. Polynomially bounded register machines and P. Justifying the class P.

  • Nondeterminism Queries Reductions NP NP and other classes defined using Turing machines SAT and boolean formulas SAT is NP-complete The Hamiltonian circuit problem 3-Colourability of graphs

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