Related papers: Synchronisation of running sums of automatic seque…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
We propose a unified definition for synchronization. By example we show that the synchronization phenomena discussed in the dynamical systems literature can be described within the framework of this definition.
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
We count the number of alignments of $N \ge 1$ sequences when match-up types are from a specified set $S\subseteq \mathbb{N}^N$. Equivalently, we count the number of nonnegative integer matrices whose rows sum to a given fixed vector and…
Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
This paper provides an introduction to the design of augmented data structures that offer an efficient representation of a mathematical sequence and fast sequential summation algorithms, which guarantee both logarithmic running time and…
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
Automated metrics for Machine Translation have made significant progress, with the goal of replacing expensive and time-consuming human evaluations. These metrics are typically assessed by their correlation with human judgments, which…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain…
Summarizing texts is not a straightforward task. Before even considering text summarization, one should determine what kind of summary is expected. How much should the information be compressed? Is it relevant to reformulate or should the…
Summaries are important when it comes to process huge amounts of information. Their most important benefit is saving time, which we do not have much nowadays. Therefore, a summary must be short, representative and readable. Generating…
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…
The purpose of this paper is to study subsequences of synchronizing $k$-automatic sequences $a(n)$ along Piatetski-Shapiro sequences $\lfloor n^c \rfloor$ with non-integer $c>1$. In particular, we show that $a(\lfloor n^c \rfloor)$…
We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in…
How reliably an automatic summarization evaluation metric replicates human judgments of summary quality is quantified by system-level correlations. We identify two ways in which the definition of the system-level correlation is inconsistent…
Synchronization is ubiquitous in nature at various scales and fields. This phenomenon not only offers a window into the intrinsic harmony of complex systems, but also serves as a robust probe for many-body quantum systems. One such system…
This paper proposes a technique to specify and verify whether a loop can be parallelised. Our approach can be used as an additional step in a parallelising compiler to verify user annotations about loop dependences. Essentially, our…