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NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
Whether randomized algorithms with polynomial time complexity can be the fastest algorithm for some problems is an open question known as the P versus NP problem. There are two large classes of such algorithms: Monte Carlo algorithms return a correct answer with high probability. E.g.
Accepting natural language questions makes the system more user-friendly, but harder to implement, as there are a variety of question types and the system will have to identify the correct one in order to give a sensible answer. Assigning a question type to the question is a crucial task; the entire answer extraction process relies on finding ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
A decision problem is a question which, for every input in some infinite set of inputs, requires a "yes" or "no" answer. [2] Those inputs can be numbers (for example, the decision problem "is the input a prime number?") or values of some other kind, such as strings of a formal language.
Methods from empirical algorithmics complement theoretical methods for the analysis of algorithms. [2] Through the principled application of empirical methods, particularly from statistics, it is often possible to obtain insights into the behavior of algorithms such as high-performance heuristic algorithms for hard combinatorial problems that are (currently) inaccessible to theoretical ...
There are several broadly recognized algorithmic techniques that offer a proven method or process for designing and constructing algorithms. Different techniques may be used depending on the objective, which may include searching, sorting, mathematical optimization, constraint satisfaction, categorization, analysis, and prediction.
Algorithm engineering does not intend to replace or compete with algorithm theory, but tries to enrich, refine and reinforce its formal approaches with experimental algorithmics (also called empirical algorithmics). This way it can provide new insights into the efficiency and performance of algorithms in cases where