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Instead, computer scientists rely on reductions to formally relate the hardness of a new or complicated problem to a computational hardness assumption about a problem that is better-understood. Computational hardness assumptions are of particular importance in cryptography .
In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to be hard in general, by efficiently exploring the usually large solution space of these instances. Combinatorial search algorithms achieve this efficiency by reducing the effective size of the ...
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
Researchers and practitioners use metaheuristic search techniques, which impose little assumptions on the problem structure, to find near-optimal or "good-enough" solutions. [1] SBSE problems can be divided into two types: black-box optimization problems, for example, assigning people to tasks (a typical combinatorial optimization problem).
Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers. Rational numbers can be written in the form p/q, where p and ...
Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.
hard problem Computational complexity theory focuses on classifying computational problems according to their inherent difficulty, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. hash function
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