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The cyclic redundancy check (CRC) is based on division in the ring of polynomials over the finite field GF (2) (the integers modulo 2 ), that is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around. Any string of bits can be interpreted as the coefficients of a message polynomial of this ...
Quadratic unconstrained binary optimization. Quadratic unconstrained binary optimization ( QUBO ), also known as unconstrained binary quadratic programming ( UBQP ), is a combinatorial optimization problem with a wide range of applications from finance and economics to machine learning. [1] QUBO is an NP hard problem, and for many classical ...
LCP problems can be solved also by the criss-cross algorithm, conversely, for linear complementarity problems, the criss-cross algorithm terminates finitely only if the matrix is a sufficient matrix. [8] [9] A sufficient matrix is a generalization both of a positive-definite matrix and of a P-matrix , whose principal minors are each positive.
The necklace problem involves the reconstruction of a necklace of beads, each of which is either black or white, from partial information. The information specifies how many copies the necklace contains of each possible arrangement of black beads. For instance, for , the specified information gives the number of pairs of black beads that are ...
In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses . In other words, if is a subset of a group , then , the subgroup generated by , is the smallest subgroup of ...
Generation of primes. In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers. For relatively small numbers, it is possible to just apply trial division to ...
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