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In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the…
Languages based on the theory of timed automata are a well established approach for modelling and analysing real-time systems, with many applications both in industrial and academic context. Model checking for timed automata has been…
In this paper, we study the model-checking and parameter synthesis problems of the logic TCTL over discrete-timed automata where parameters are allowed both in the model (timed automaton) and in the property (temporal formula). Our results…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
We survey the classical results of the Dirichlet Approximation Theorem.
Understanding the accuracy limits of machine learning algorithms is essential for data scientists to properly measure performance so they can continually improve their models' predictive capabilities. This study empirically verified the…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
Simulations of strongly interacting lattice field theories are typically performed using Markov chain Monte Carlo algorithms. Therefore estimators of statistical errors must incorporate the effect of autocorrelations by integrating the…
An explicit subconvex bound for the Riemann zeta function $\zeta(s)$ on the critical line $s=1/2+it$ is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
The \v{C}ern\'y's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n-11)^2. We prove this conjecture for a class of automata preserving certain properties of intervals…
Recent work on language model self-improvement shows that models can refine their own reasoning through reflection, verification, debate, or self-generated rewards. However, most existing approaches rely on external critics, learned reward…
In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory.…
This report discusses the improved bound of the cluster expansion, recently proposed by Procacci and Yuhjtman (Lett. Math. Phys. 107, 31, 2017). Brydges and Helmuth noticed the relevance of Kruskal's algorithm, which allows to streamline…
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
This work improves monolingual sentence alignment for text simplification, specifically for text in standard and simple Wikipedia. We introduce a convolutional neural network structure to model similarity between two sentences. Due to the…
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
A word $w$ is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if $w$ sends all states of the automaton to a unique state. In 1964 Jan \v{C}erny found a sequence of n-state complete DFA…