Using the fact that the factorization of xN -1over GF(2) is especially explicit, we completely establish the distributions and the expected values of the linear complexity and the k-error linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a ...
In many simple integral domains, such as $\mathbb{Z}$ or $\mathbb{Z}[i]$, there is a straightforward procedure to determine if an element is prime by simply reducing to a direct check of finitely many potential divisors. Despite the fact that such a naive approach does not immediately ...
The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining met
For an arbitrary number of pulses, Lerdahl and Jackendoff 's hierarchy thus derives from a (non-unique) tree-like structure built upon the prime factorization of N. For the sake of simplicity, however, we only consider the case of rhythms whose length is a power of two, which is relevant...
Problem 6: Factorization 1 2 3 4 5 6 7 8 9 10 11 12 input: n-bit integer X // see not below the algorithm output: list of prime factors and their multiplicity acc = X for i = 2 ... sqrt( X ) count = 0 while acc % i == 0 ...
Given two k-graphs H and F, a perfect F-packing in H is a collection of vertex-disjoint copies of F in H which together cover all the vertices in H. In the case when F is a single edge, a perfect F-packing is simply a perfect matching. For a given fixed F, it is often the...
integer factoring or primality testing (see prime number). For an n-bit num- ber, trial division can take time up to 2 n/2 , which is exponential time rather than polynomial time in n. Thus, even for moderate values of n (e.g. n = ...
Let\(x^{\prime }>0\)be a positive integer. There is a linear time reduction which transforms instances (G,b,x,k) ofCollapsed k-Corewithx= 0 into equivalent instances\((G^{\prime },b,x^{\prime },k)\)ofCollapsed k-Core. Moreover, the degeneracy of\(G^{\prime }\)is at most...
Prime_Factorization Added runtime input (#1301) May 25, 2019 Prime_Number Added Implementation of Prime Numbers using JS (#1723) Mar 3, 2020 Prims_Algorithm Prims Algorithm implementation in Dart (#2785) May 30, 2020 Priority_Queue Priority_Queue.py Mar 30, 2020 Pythagorean_Quadruples Added ...
The field Ident represents the unique identification number of the user; the field Loc represents the position when the user initiates the request; Clastands for POI category; Utime represents the time point when the user sends the request; λrepresents a large odd prime number. Definition 4. ...