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New algorithms could enhance autonomous spacecraft safety

For humans throughout history, the sky has evoked thoughts of a vast emptiness, of a great vacant dome punctuated during the day by the sun, and at night by numerous tiny spots of light (and periodically by the moon). As ...

AI accelerates discovery of next-gen polymers

Nylon, Teflon, Kevlar. These are just a few familiar polymers—large-molecule chemical compounds—that have changed the world. From Teflon-coated frying pans to 3D printing, polymers are vital to creating the systems that ...

Generalized splitting-ring number theoretic transform

Number theoretic transform (NTT) is widely recognized as the most efficient method for computing polynomial multiplication with high dimension and integral coefficients, due to its quasilinear complexity.

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Algorithm

In mathematics, computing, linguistics, and related subjects, an algorithm is a finite sequence of instructions, an explicit, step-by-step procedure for solving a problem, often used for calculation and data processing. It is formally a type of effective method in which a list of well-defined instructions for completing a task, will when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end-state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as probabilistic algorithms, incorporate randomness.

A partial formalization of the concept began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" (Kleene 1943:274) or "effective method" (Rosser 1939:225); those formalizations included the Gödel-Herbrand-Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

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