This article is about decision problems in complexity theory. For the decision problem in formal logic, see Entscheidungsproblem. For analysis of the process of making choices, see Decision theory.
A decision problem has only two possible outputs (yes or no) on any input.
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem. A decision procedure for the decision problem "given two numbers x and y, does x evenly divide y?" would give the steps for determining whether x evenly divides y. One such algorithm is long division. If the remainder is zero the answer is 'yes', otherwise it is 'no'. A decision problem which can be solved by an algorithm is called decidable.
Decision problems typically appear in mathematical questions of decidability, that is, the question of the existence of an effective method to determine the existence of some object or its membership in a set; some of the most important problems in mathematics are undecidable.
The field of computational complexity categorizes decidable decision problems by how difficult they are to solve. "Difficult", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem. The field of recursion theory, meanwhile, categorizes undecidable decision problems by Turing degree, which is a measure of the noncomputability inherent in any solution.
theory, a decisionproblem is a computational problem that can be posed as a yes–no question of the input values. An example of a decisionproblem is deciding...
random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via dynamic programming. MDPs were...
(German for 'decisionproblem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for...
make decisions about problems that may be rapidly changing and not easily specified in advance—i.e., unstructured and semi-structured decisionproblems. Decision...
of a decisionproblem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decisionproblem that...
instance of this problem is a rather concrete utterance, which can serve as the input for a decisionproblem. For example, consider the problem of primality...
model a variety of real-world sequential decision processes. Applications include robot navigation problems, machine maintenance, and planning under uncertainty...
theory and computational complexity theory, an undecidable problem is a decisionproblem for which it is proved to be impossible to construct an algorithm...
is the right thing to do? Philippa Foot introduced this genre of decisionproblems in 1967 as part of an analysis of debates on abortion and the doctrine...
knapsack problem has been studied for more than a century, with early works dating as far back as 1897. Knapsack problems appear in real-world decision-making...
allocation. The existence of a solution to a CSP can be viewed as a decisionproblem. This can be decided by finding a solution, or failing to find a solution...
Unsolved problem in computer science: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? (more unsolved...
could introduce suitable decisionproblems, the problem is more naturally characterized as an optimization problem. Counting problem (complexity) – Type of...
computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decisionproblems that...
enlarged), and solving the decisionproblem of testing whether a graph contains a clique larger than a given size. The clique problem arises in the following...
natural decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem, and...
representation. A decisionproblem is a computational problem where the answer for every instance is either yes or no. An example of a decisionproblem is primality...
The subset sum problem (SSP) is a decisionproblem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers...
introduce suitable decisionproblems, the problem is then more naturally characterized as an optimization problem. An NP-optimization problem (NPO) is a combinatorial...
programming invention can possibly perform perfectly. The halting problem is a decisionproblem about properties of computer programs on a fixed Turing-complete...
testing and parameter estimation, are special cases of the general decisionproblem. Wald's paper renewed and synthesized many concepts of statistical...
must be formulated as a decisionproblem. The input to the decisionproblem is a pair of graphs G and H. The answer to the problem is positive if H is isomorphic...
study decisionproblems. It can be visualized as a Turing machine with a black box, called an oracle, which is able to solve certain problems in a single...
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