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In cryptography, Galois/Counter Mode (GCM) [1] is a mode of operation for symmetric-key cryptographic block ciphers which is widely adopted for its performance. GCM throughput rates for state-of-the-art, high-speed communication channels can be achieved with inexpensive hardware resources.
The W hierarchy is a collection of computational complexity classes. A parameterized problem is in the class W[i], if every instance (,) can be transformed (in fpt-time) to a combinatorial circuit that has weft at most i, such that (,) if and only if there is a satisfying assignment to the inputs that assigns 1 to exactly k inputs.
In machine learning, hyperparameter optimization [1] or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts.
The full potential of parameterized approximation algorithms is utilized when a given optimization problem is shown to admit an α-approximation algorithm running in () time, while in contrast the problem neither has a polynomial-time α-approximation algorithm (under some complexity assumption, e.g., ), nor an FPT algorithm for the given parameter k (i.e., it is at least W[1]-hard).
In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.).
A typical picture does not resemble a random bitmap. In theoretical computer science , smoothed analysis is a way of measuring the complexity of an algorithm . Since its introduction in 2001, smoothed analysis has been used as a basis for considerable research, for problems ranging from mathematical programming , numerical analysis , machine ...
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
The next-state relation Tick sets clock′ (the value of clock in the next state) to 1 if clock is 0, and 0 if clock is 1. The state predicate Init is true if the value of clock is either 0 or 1. Spec is a temporal formula asserting all behaviours of one-bit clock must initially satisfy Init and have all steps either match Tick or be stuttering ...