Related papers: Reset thresholds of automata with two cycle length…
The repetition threshold is the smallest real number $\alpha$ such that there exists an infinite word over a $k$-letter alphabet that avoids repetition of exponent strictly greater than $\alpha$. This notion can be generalized to graph…
Standard techniques for treating linear recurrences no longer apply for quadratic recurrences. It is not hard to determine asymptotics for a specific parametrized model over a wide domain of values (all $p \neq 1/2$ here). The gap between…
We follow language theoretic approach to synchronizing automata and \v{C}ern\'{y}'s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a…
Ultimate bounds on the maximum operating frequency of networks of quantum dot cellular automata devices have yet to be established. We consider the adiabaticity of such networks in the two-state approximation where clocking is achieved via…
Dynamic quantum circuits generate states that depend on the measurement results obtained during circuit execution. To date such a quantum computing model has mainly been implemented with qubit-based superconducting hardware utilizing reset…
Computing the smallest number $q$ such that the vertices of a given graph can be properly $q$-colored is one of the oldest and most fundamental problems in combinatorial optimization. The $q$-Coloring problem has been studied intensively…
By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset…
Long quasi-cyclic codes of any fixed index $>1$ have been shown to be asymptotically good, depending on Artin primitive root conjecture in (A. Alahmadi, C. G\"uneri, H. Shoaib, P. Sol\'e, 2017). We use this recent result to construct good…
Coherence times for superconducting qubits have greatly improved over time. Moreover, small logical qubit architectures using engineered dissipation have shown great promise for further improvements in the coherence of a logical qubit…
A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors…
Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let $p$ be a prime with $p\ge 7$. We determine the…
Quantum synchronization has been a subject of intensive research in the last decade. In this work, we propose a quantum Li\'enard system whose classical equivalent features two limit cycles to one of which the system will converge. In the…
The Erd\H{o}s-Gy\'arf\'as number $f(n, p, q)$ is the smallest number of colors needed to color the edges of the complete graph $K_n$ so that all of its $p$-clique spans at least $q$ colors. In this paper we improve the best known upper…
We introduce and investigate forgetting 1-limited automata, which are single-tape Turing machines that, when visiting a cell for the first time, replace the input symbol in it by a fixed symbol, so forgetting the original contents. These…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We calculate one-loop renormalization factors of bilinear operators made of physical quark fields for domain-wall QCD. We find that finite parts of such renormalization factors have reasonable values at 1-loop except an overlap factor…
Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…
Many sequences of $p$-adic integers project modulo $p^\alpha$ to $p$-automatic sequences for every $\alpha \geq 0$. Examples include algebraic sequences of integers, which satisfy this property for every prime $p$, and some cocycle…
We introduce the fully-dynamic conflict-free coloring problem for a set $S$ of intervals in $\mathbb{R}^1$ with respect to points, where the goal is to maintain a conflict-free coloring for$S$ under insertions and deletions. A coloring is…
We extend the resummation of dimensionally-regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that…