DECISION PROBLEM Meaning and
Definition
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A decision problem, in computer science and mathematics, is a specific type of computational problem that requires a yes-or-no answer based on a given input. It involves determining whether a certain property or condition holds for a given input or set of inputs. Decision problems are fundamental in the study of algorithms, complexity theory, and computability.
Formally, a decision problem can be described as a binary relation R between inputs and outputs, where for each input, the relation determines whether the output is "yes" or "no." The goal is to find an algorithm or process that can correctly determine the answer for any given input.
Decision problems can vary in complexity, ranging from simple problems with efficient algorithms to undecidable problems with no algorithm that can solve them for all inputs. Complexity theory classifies decision problems based on their computational difficulty, typically measured by the amount of resources, such as time or space, required to solve them.
Decision problems find applications in various fields, including computer science, mathematics, artificial intelligence, and optimization. They are often used as fundamental building blocks for designing and analyzing algorithms, or as theoretical tools to understand the limits and capabilities of computational systems.
In summary, a decision problem is a specific type of computational problem that seeks a yes-or-no answer based on a given input. It involves determining whether a certain property or condition holds for the given input, and serves as a foundational concept in the study of algorithms, complexity theory, and computability.
Common Misspellings for DECISION PROBLEM
- secision problem
- xecision problem
- cecision problem
- fecision problem
- recision problem
- eecision problem
- dwcision problem
- dscision problem
- ddcision problem
- drcision problem
- d4cision problem
- d3cision problem
- dexision problem
- devision problem
- defision problem
- dedision problem
- decusion problem
- decjsion problem
- decksion problem
- decosion problem
Etymology of DECISION PROBLEM
The word "decision problem" originated in the field of mathematics, particularly in the area of computability theory. The term was first introduced by the German mathematician David Hilbert in the 1928 conference on "Mathematical Problems" in Bologna, Italy.
The etymology of the word itself can be broken down as follows:
1. Decision: The term "decision" comes from the Latin word "decidere", which means "to cut off" or "to determine". It refers to the act of making a choice or reaching a conclusion.
2. Problem: The word "problem" has its roots in the Greek word "problema", which means "something thrown forward" or "a question to be answered". It refers to a situation or issue that requires a solution.
When combined, "decision problem" refers to a specific type of problem that requires making a decision or determining the answer.
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