In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question based on the given input values. An example of a decision problem is deciding with the help of an algorithm whether a given natural number is prime.

Decision problem, for a class of questions in mathematics and formal logic, the problem of finding, after choosing any question of the class, an algorithm or repetitive procedure that will yield a definite answer, “yes” or “no,” to that question.

Using the deduction theorem, the Entscheidungsproblem encompasses the more general problem of deciding whether a given first-order sentence is entailed by a given finite set of sentences, but validity in first-order theories with infinitely many axioms cannot be directly reduced to the Entscheidungsproblem.

A decision problem has only two possible outputs, yes or no (or alternately 1 or 0) on any input. In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer. The answer is dependent on the values of …

1. Introduction: The Classical Decision Problem 1.1 The Original Problem The original classical decision problem can be stated in several equivalent ways. – The satisfiability problem (or the consistency problem) for first-order logic: given a first-order formula, decide if it is consistent.

In recursion theory and computational complexity theory, a decision problem is a yes-or-no question on specified sets of inputs. For example, the problem "given two natural numbers x and y, does x evenly divide y?" is a decision problem. The answer can be either "yes" or "no" and depends upon the values of x and y.

2025年2月16日 · Decision Problem Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the Entscheidungsproblem (which, not so coincidentally, is …

The Entscheidungsproblem, or Decision Problem, states that given all the axioms of math, there is an algorithm that can tell if a proposition is provable. During the 1930s, Alonzo Church, Stephen Kleene, Kurt

2016年1月10日 · Decision problems are meaningful only when the notion of an effective computational procedure is suitably formalized, as in the theory of algorithms. A positive solution to a decision problem consists of giving an algorithm for solving it, the problem is then said to be decidable or solvable.

In this course we will deal with four types of computational problems: decision prob-lems, search problems, optimization problems, and counting problems.1 For the mo-ment, we will discuss decision and search problem. In a decision problem, given an input x 2 f0; 1g , we are required to give a YES/NO answer.