Related papers: The $k$-error linear complexity distribution for $…
We recently introduced the graph invariant twin-width, and showed that first-order model checking can be solved in time $f(d,k)n$ for $n$-vertex graphs given with a witness that the twin-width is at most $d$, called $d$-contraction sequence…
This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the…
The problem of whether and how one can compute the twin-width of a graph -- along with an accompanying contraction sequence -- lies at the forefront of the area of algorithmic model theory. While significant effort has been aimed at…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…
In this work we introduce a new notion called opacity complexity to measure the complexity of automatic sequences. We study basic properties of this notion, and exhibit an algorithm to compute it. As applications, we compute the opacity…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
In this paper, we determine the linear complexity of a class of new binary cyclotomic sequences of period pn constructed by Z. Xiao et al. (Des. Codes Cryptogr. DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high linear…
In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms…
While finding a path between two nodes is the basis for several applications, the need for alternative paths also may have various motivations. For instance, this can be of interest for ensuring reliability in a telecommunications network,…
A graph $G$ is said to be a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. It is well established that the recognition problem for $(k,\ell)$-graphs is NP-complete whenever $k \geq 3$ or…
The generalized egg dropping problem is a classic challenge in sequential decision-making. Standard dynamic programming evaluates the minimax minimum number of tests in $\mathcal{O}(K \cdot N^2)$ time. A known approach formulates the…
This work shows that the cryptanalysis of the shrinking generator requires fewer intercepted bits than what indicated by the linear complexity. Indeed, whereas the linear complexity of shrunken sequences is between $A \cdot 2^(S-2)$ and $A…
In most of the network coding problems with $k$ messages, the existence of binary network coding solution over $\mathbb{F}_2$ depends on the existence of adequate sets of $k$-dimensional binary vectors such that each set comprises of…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…
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…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…