# 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 --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/600-toc/toc.topics.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.