Related papers: A Case Study in Analytic Protocol Analysis in ACL2
In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time…
We consider the development of adaptive, instance-dependent algorithms for interactive decision making (bandits, reinforcement learning, and beyond) that, rather than only performing well in the worst case, adapt to favorable properties of…
We derive explicit asymptotic expansions of the density of the supremum of a strictly stable process when the index $\alpha$ is not rational. In the case when parameters $\alpha$ and $\rho=\p(X_1>0)$ satisfy $\rho+k=l/\alpha$ for some…
We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…
Augmented Language Models (ALMs) blend the reasoning capabilities of Large Language Models (LLMs) with tools that allow for knowledge retrieval and action execution. Existing ALM systems trigger LLM thought processes while pulling…
Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive…
We investigate asymptotic behaviour of averaging operators for actions of simple rank-one Lie groups. It was previously known that these averaging operators converge almost everywhere, and we establish a more precise asymptotic formula that…
We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…
As Graphics Processing Units (GPUs) have gained in capability and GPU development environments have matured, developers are increasingly turning to the GPU to off-load the main host CPU of numerically-intensive, parallelizable computations.…
We present a methodology for formal verification of arithmetic RTL designs that combines sequential logic equivalence checking with interactive theorem proving. An intermediate model of a Verilog module is hand-coded in Restricted…
The set of all error--correcting block codes over a fixed alphabet with $q$ letters determines a recursively enumerable set of rational points in the unit square with coordinates $(R,\delta)$:= (relative transmission rate, relative minimal…
We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…
This paper considers the problem of real-time control and learning in dynamic systems subjected to parametric uncertainties. We propose a combination of a Reinforcement Learning (RL) based policy in the outer loop suitably chosen to ensure…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of $C_0$-semigroups to obtain a…
Congestion control in the current Internet is accomplished mainly by TCP/IP. To understand the macroscopic network behavior that results from TCP/IP and similar end-to-end protocols, one main analytic technique is to show that the the…
Large Reasoning Models (LRMs) often suffer from the ``over-thinking'' problem, generating unnecessarily long reasoning on simple tasks. Some strategies have been proposed to mitigate this issue, such as length penalties or routing…
RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new…
Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…