otsustusülesannetel

Otsustusülesanded, known in English as decision problems or decision tasks, are a fundamental concept in computer science and mathematics, particularly in the field of computability theory and computational complexity. An otsustusülesanne is a problem that can be answered with a simple "yes" or "no". Unlike optimization problems that seek the best solution among many, or search problems that aim to find a specific item, decision problems have only two possible outcomes.

For instance, the "Traveling Salesperson Problem" is an optimization problem where the goal is to find the shortest possible route that visits a given set of cities and returns to the origin city. However, a corresponding otsustusülesanne for this problem would be: "Does there exist a route that visits all cities and returns to the origin with a total length less than or equal to K kilometers?". The answer to this question is either "yes" or "no".

The study of otsustusülesanded is crucial for understanding the limits of what can be computed efficiently. Algorithms are often designed to solve these problems, and their efficiency is measured by how quickly they can arrive at a "yes" or "no" answer as the size of the input grows. This leads to classifications like P (problems solvable in polynomial time) and NP (problems for which a "yes" answer can be verified in polynomial time), which are central to computational complexity theory. Understanding the nature of otsustusülesanded helps researchers categorize problems by their inherent difficulty and guides the search for efficient algorithms.