Related papers: The 4-error linear complexity distribution for $2^…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Let $1<g_1<\ldots<g_{\varphi(p-1)}<p-1$ be the ordered primitive roots modulo~$p$. We study the pseudorandomness of the binary sequence $(s_n)$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod 2$, $n=0,1,\ldots$. In particular, we study the…
In this paper, we consider the Integrated Completed Likelihood (ICL) as a useful criterion for estimating the number of changes in the underlying distribution of data in problems where detecting the precise location of these changes is the…
A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the…
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
In this paper, we seek a natural problem and a natural distribution of instances such that any $O(n^{c-\epsilon})$-time algorithm fails to solve most instances drawn from the distribution, while the problem admits an $n^{c+o(1)}$-time…
We identify a period-4 measurement schedule for the checks of the Bacon-Shor code that fully covers spacetime with constant-weight detectors, and is numerically observed to provide the code with a threshold. Unlike previous approaches, our…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed…
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set…
A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
Pseudorandom number generators are required to generate pseudorandom numbers which have good statistical properties as well as unpredictability in cryptography. An m-sequence is a linear feedback shift register sequence with maximal period…
Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequences of period $4p$ with optimal autocorrelation magnitude was constructed in \cite{W. Su}. Later, Fan showed that the linear complexity of this class of sequences is…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We investigate the complexity of logistic regression models which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with…
This work considers the problem of output-sensitive listing of occurrences of $2k$-cycles for fixed constant $k\geq 2$ in an undirected host graph with $m$ edges and $t$ $2k$-cycles. Recent work of Jin and Xu (and independently Abboud,…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…