Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding whether a given natural number is prime. Another example is the problem, "given two numbers x and y, does x evenly divide y?"
Many-one reductionIn computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances of one decision problem (whether an instance is in L1{\displaystyle L_{1}}) to another decision problem (whether an instance is in L2{\displaystyle L_{2}}) using a computable function.
Turing reductionIn computability theory, a Turing reduction from a decision problemA{\displaystyle A} to a decision problem B{\displaystyle B} is an oracle machine that decides problem A{\displaystyle A} given an oracle for B{\displaystyle B} (Rogers 1967, Soare 1987) in finitely many steps. It can be understood as an algorithm that could be used to solve A{\displaystyle A} if it had access to a subroutine for solving B{\displaystyle B}.Truth-table reductionIn computability theory, a truth-table reduction is a type of reduction from a decision problemA{\displaystyle A} to a decision problem B{\displaystyle B}. To solve a problem in A{\displaystyle A}, the reduction describes the answer to A{\displaystyle A} as a boolean formula or truth table of some finite number of queries to B{\displaystyle B}. Truth-table reductions are related to Turing reductions, and strictly weaker.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer and is solvable by mechanical application of mathematical steps, such as an algorithm.
Reduction (complexity)In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B, if an algorithm for solving problem B efficiently (if it exists) could also be used as a subroutine to solve problem A efficiently.
Complexity classIn computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory.
Complete (complexity)In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or "most expressive") problems in the complexity class.
AlgorithmIn mathematics and computer science, an algorithm () is any well-defined set of instructions that when followed terminates after a finite number of steps that comprise a solution to a given computational problem. Advanced algorithms may utilize loops and involve many conditionals that decide the next step based on the inputs provided, resulting in long sequences of steps before halting, but all algorithms terminate by definition.PolynomialIn mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate x {\displaystyle x} is x 2 − 4 x + 7 {\displaystyle x^{2}-4x+7} .
ContrapositionMathematical logic conceptIn logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalentcontrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequentnegated and swapped. Conditional statementP→Q{\displaystyle P ightarrow Q}.
Function (computer programming)In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed interface and behavior and can be invoked multiple times. Callable units provide a powerful programming tool. The primary purpose is to enable the decomposition of a large and/or complicated problem into chunks that have relatively low cognitive load.*As an Amazon Associate I earn from qualifying purchases.