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Worked examples are step-by-step solutions to problems in a specific domain, offered to students to acquire domain-specific problem-solving skills. The effectiveness of worked examples could be enhanced by combining them with…
This paper contains a small improvement to the explicit bounds on the growth of the function $S(T)$. It is shown how more substantial improvements are possible if one has better explicit bounds on the growth of $|\zeta(\frac{1}{2}+it)|$.
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been…
We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp(1.96 \times 10^{19})$, which is significantly below the conjectured value of $\approx \exp(5.15 \times…
We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…
As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then…
The incorporation of pseudo data in the training of grammatical error correction models has been one of the main factors in improving the performance of such models. However, consensus is lacking on experimental configurations, namely,…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…
Going beyond mimicking limited human experiences, recent studies show initial evidence that, like humans, large language models (LLMs) are capable of improving their abilities purely by self-correction, i.e., correcting previous responses…
We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…
Upon re-examining Arnold's established lemma for explaining his famous limit problem, we have determined that while the lemma itself is correct, there is a defect in the original geometric proof. In this paper, we prove the correctness of…
We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite…
The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human…
Active learning of finite automata has been vigorously pursued for the purposes of analysis and explanation of black-box systems. In this paper, we study an L*-style learning algorithm for weighted automata over the max-plus semiring. The…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
In this overview article we will consider the deliberate restarting of algorithms, a meta technique, in order to improve the algorithm's performance, e.g., convergence rates or approximation guarantees. One of the major advantages is that…