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R vs. RE problem, where R is analog of class P, and RE is analog class NP. These classes are not equal, because undecidable but verifiable problems do exist, for example, Hilbert's tenth problem which is RE-complete. [57] A similar problem exists in the theory of algebraic complexity: VP vs. VNP problem. This problem has not been solved yet.
The Boolean satisfiability problem (SAT) asks to determine if a propositional formula (example depicted) can be made true by an appropriate assignment ("solution") of truth values to its variables. While it is easy to verify whether a given assignment renders the formula true , [ 1 ] no essentially faster method to find a satisfying assignment ...
The second, usually called Truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.
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The question then is, whether there exists an algorithm that maps instances to solutions. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n. An example of a computational problem without a solution is the Halting problem. Computational problems ...
Measurements generally have a small amount of error, and repeated measurements of the same item will generally result in slight differences in readings. These differences can be analyzed, and follow certain known mathematical and statistical properties.
In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process.
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...