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 the input parameters. 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.
Decision problem
Questions and Answers
Q: What is a decision problem?
A: A decision problem is a question in some formal system with a yes-or-no answer, dependent on the values of input parameters.
Q: In what fields of study do decision problems appear?
A: Decision problems typically appear in mathematical questions of decidability.
Q: What is the meaning of decidability?
A: Decidability refers to the question of the existence of an effective method to determine the existence of some object or its membership in a set.
Q: Are all problems in mathematics decidable?
A: No, some of the most important problems in mathematics are undecidable.
Q: What is an undecidable problem?
A: An undecidable problem is a problem for which no algorithm exists that can always provide a yes-or-no answer within a finite amount of time.
Q: Is the answer to a decision problem always yes or no?
A: Yes, the answer to a decision problem is always yes or no.
Q: What does the answer to a decision problem depend on?
A: The answer to a decision problem depends on the values of the input parameters.