Related papers: Arithmetic Autocorrelation of Binary $m$-Sequences
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…
Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident. It is commonly believed that such over-confidence is mainly due…
We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
The generalized cyclotomic binary sequences $S=S(a, b, c)$ with period $n=pq$ have good autocorrelation property where $(a, b, c)\in \{0, 1\}^3$ and $p, q$ are distinct odd primes. For some cases, the sequences $S$ have ideal or optimal…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
In this paper, we study the sequences with (non-consecutive) two zero-symbols and ideal autocorrelation, which are also known as almost $m$-ary nearly perfect sequences. We show that these sequences are equivalent to $\ell$-partial direct…
Bounds for $\max\{m,\tilde{m}\}$ subject to $m,\tilde{m} \in \mathbb{Z}\cap[1,p)$, $p$ prime, $z$ indivisible by $p$, $m\tilde{m}\equiv z\bmod p$ and $m$ belonging to some fixed Beatty sequence $\{ \lfloor n\alpha+\beta \rfloor :…
Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time's dependence on…
We show an $\widetilde{O}(m^{1.5} \epsilon^{-1})$ time algorithm that on a graph with $m$ edges and $n$ vertices outputs its spanning tree count up to a multiplicative $(1+\epsilon)$ factor with high probability, improving on the previous…
Suppose that $k$ series, all having the same autocorrelation function, are observed in parallel at $n$ points in time or space. From a single series of moderate length, the autocorrelation parameter $\beta$ can be estimated with limited…
In this paper we employ methods from Statistical Mechanics to model temporal correlations in time series. We put forward a methodology based on the Maximum Entropy principle to generate ensembles of time series constrained to preserve part…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
We identify a cyclic property of rotation sequences involving piecewise displacements $\beta$ about arbitrary axes in three dimensions. Specifically, when transformation to the toggling frame is applied successively $m$ times, for…
Pseudorandom binary sequences with optimal balance and autocorrelation have many applications in stream cipher, communication, coding theory, etc. It is known that binary sequences with three-level autocorrelation should have an almost…
Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…