Related papers: Knuth's Moves on Timed Words
Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the…
We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…
A subshift of finite type over finitely many symbols can be described as a collection of all infinite walks on a digraph with at most a single edge from a vertex to another. The associated finite set $\F$ of forbidden words is a constraint…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
We consider the length of the longest word definable in FO and MSO via a formula of size n. For both logics we obtain as an upper bound for this number an exponential tower of height linear in n. We prove this by counting types with respect…
In the past few decades, there has been an explosion in the amount of available data produced from various sources with different topics. The availability of this enormous data necessitates us to adopt effective computational tools to…
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi\'nski gasket that…
We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.
Quantum Algorithms have long captured the imagination of computer scientists and physicists primarily because of the speed up achieved by them over their classical counterparts using principles of quantum mechanics. Entanglement is believed…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
Exploiting higher-order derivatives in convex optimization is known at least since 1970's. In each iteration higher-order (also called tensor) methods minimize a regularized Taylor expansion of the objective function, which leads to faster…
We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word $w$ of length $n$ over an alphabet of cardinality $k$, $w$ can be…
We construct an algorithm that reduces the complexity for computing generalized Dedekind sums from exponential to polynomial time. We do so by using an efficient word rewriting process in group theory.
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
A statistical model for segmentation and word discovery in continuous speech is presented. An incremental unsupervised learning algorithm to infer word boundaries based on this model is described. Results of empirical tests showing that the…
In this paper, we propose an alternative to deep neural networks for semantic information retrieval for the case of long documents. This new approach exploiting clustering techniques to take into account the meaning of words in Information…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
We describe a visualization tool that can be used to view the change in meaning of words over time. The tool makes use of existing (static) word embedding datasets together with a timestamped $n$-gram corpus to create {\em temporal} word…
Using a vocabulary that is shared across languages is common practice in Multilingual Neural Machine Translation (MNMT). In addition to its simple design, shared tokens play an important role in positive knowledge transfer, assuming that…
Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…