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Decision problem

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In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. [1]

43 relations: Algorithm, ALL (complexity), Alphabet (formal languages), Boolean satisfiability problem, Co-NP-complete, Complement (complexity), Complete (complexity), Complexity class, Computability theory, Computational complexity theory, Computational problem, Computational resource, Counting problem (complexity), Decidability (logic), Decision problem, Effective method, Formal language, Formal system, Function problem, Gödel numbering, Halting problem, Hartley Rogers, Jr., Indicator function, List of undecidable problems, Long division, Many-one reduction, Michael Sipser, NP (complexity), NP-completeness, Optimization problem, Partial function, Polynomial-time reduction, Primality test, Recursive set, Recursively enumerable set, Search problem, String (computer science), Time complexity, Turing degree, Undecidable problem, Word problem (mathematics), Yes–no question, Zohar Manna.

Algorithm

In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed.

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ALL (complexity)

In computability and complexity theory, ALL is the class of all decision problems.

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Alphabet (formal languages)

In formal language theory, a non-empty set is called alphabet when its intended use in string operations shall be indicated.

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Boolean satisfiability problem

In computer science, the Boolean Satisfiability Problem (sometimes called Propositional Satisfiability Problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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Co-NP-complete

In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP complete problem with only polynomial overhead.

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Complement (complexity)

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers.

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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.

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Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

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Computability theory

Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Computational problem

In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve.

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Computational resource

In computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems.

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Counting problem (complexity)

In computational complexity theory and computability theory, a counting problem is a type of computational problem.

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Decidability (logic)

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value (instead of looping indefinitely).

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Decision problem

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.

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Effective method

In logic, mathematics and computer science, especially metalogic and computability theory, an effective methodHunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Press, 1971 or effective procedure is a procedure for solving a problem from a specific class.

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Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.

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Formal system

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics.

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Function problem

In computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem, that is, it isn't just YES or NO.

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Gödel numbering

In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.

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Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.

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Hartley Rogers, Jr.

Hartley Rogers, Jr. was a mathematician who worked in recursion theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.

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List of undecidable problems

In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is any possible program would sometimes give the wrong answer or run forever without giving any answer.

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Long division

In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand.

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Many-one reduction

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.

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Michael Sipser

Michael Fredric Sipser (born September 17, 1954) is a theoretical computer scientist who has made early contributions to computational complexity theory.

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NP (complexity)

In computational complexity theory, NP is one of the most fundamental complexity classes.

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NP-completeness

In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard.

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Optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.

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Partial function

In mathematics, a partial function from X to Y (written as) is a function, for some subset X′ of X.

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Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.

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Primality test

A primality test is an algorithm for determining whether an input number is prime.

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Recursive set

In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set.

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Recursively enumerable set

In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if.

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Search problem

In computational complexity theory and computability theory, a search problem is a type of computational problem represented by a binary relation.

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String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

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Time complexity

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the string representing the input.

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Turing degree

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.

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Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.

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Word problem (mathematics)

In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set.

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Yes–no question

In linguistics, a yes–no question, formally known as a polar question, is a question whose expected answer is either "yes" or "no".

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Zohar Manna

Zohar Manna (born 1939) is a professor of computer science at Stanford University.

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Decidability problems, Decidable problem, Decision problems, Decision procedure, Decision variant, Decision version, Solvable problem, Word problem (computability).

References

[1] https://en.wikipedia.org/wiki/Decision_problem

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