Otsustusülesanded

Otsustusülesanded, also known as decision tasks, are a class of computational problems that can be solved by an algorithm. These problems are characterized by having a yes/no answer. For example, the task of determining if a given number is prime is a decision task: the answer is either yes, it is prime, or no, it is not prime.

In computer science, the study of decision tasks is fundamental to understanding the limits of computation. Many important problems, such as the halting problem, are undecidable decision tasks, meaning no algorithm can solve them for all possible inputs.

The complexity of decision tasks is often analyzed using complexity classes. For instance, the class P contains all decision tasks that can be solved in polynomial time by a deterministic Turing machine. The class NP contains decision tasks for which a proposed solution can be verified in polynomial time by a deterministic Turing machine. The question of whether P equals NP is one of the most important open problems in theoretical computer science.

Decision tasks are ubiquitous in various fields. In artificial intelligence, they are used in areas like planning and search. In operations research, they form the basis for optimization problems. Understanding decision tasks and their properties helps in designing efficient algorithms and comprehending the inherent difficulty of computational problems.