User:Williamdemeo/Books/Complexity Theory

= Complexity Theory =

Basics

 * Computational complexity theory
 * Time complexity
 * P versus NP problem
 * Effective method

Complexity Classes

 * P (complexity)
 * NP (complexity)
 * Co-NP
 * NP-complete
 * NP-hard
 * Karp's 21 NP-complete problems
 * List of NP-complete problems

Types of Problems

 * Decision problem
 * Counting problem (complexity)
 * Search problem
 * Reduction (complexity)
 * Many-one reduction

Examples

 * Boolean satisfiability problem
 * Subset sum problem

= Computability Theory =

Logic Basics

 * First-order logic
 * Soundness
 * Completeness_(logic)
 * Consistency
 * Peano axioms

Computable and Recursive Functions

 * Computability theory
 * Computable function
 * Primitive recursive arithmetic
 * Primitive recursive function
 * Turing completeness
 * Church-Turing thesis
 * History of the Church%E2%80%93Turing thesis

Goedel's Theorems

 * G%C3%B6del%27s completeness theorem
 * G%C3%B6del%27s incompleteness theorems
 * Gentzen%27s consistency proof

= Type Theory =

Basics

 * Type theory
 * Fixed-point combinator
 * Dependent type

Functional Programming

 * Functional programming
 * Typed lambda calculus
 * Total functional programming
 * Curry-Howard correspondence
 * Corecursion