Related papers: On the greatest solution of equations in $\text{CL…

This paper explores the process calculus $\text{CLL}_R$ furtherly. First, we prove that for any equation $X=_{RS} t_X$ such that $X$ is strongly guarded in $t_X$, $\langle X|X=t_X \rangle$ is the largest solution w.r.t $\sqsubseteq_{RS}$.…

In the framework of logic labelled transition system, a variant of weak ready simulation has been presented by L\"{u}ttgen and Vogler. It has been shown that such behavioural preorder is the largest precongruence w.r.t parallel and…

In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS…

In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the…

This paper shows that guarded systems of recursive equations have unique solutions up to strong bisimilarity for any process algebra with a structural operation semantics in the ready simulation format. A similar result holds for simulation…

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…

If $$ \Delta(x) := \sum_{n\le x}c_n - Cx $$ denotes the error term in the classical Rankin-Selberg problem, then it is proved that $$ \int_0^X \Delta^4(x)\d x \ll_\epsilon X^{3+\epsilon},\quad \int_0^X \Delta_1^4(x)\d x \ll_\epsilon…

Large Language Models (LLMs) have garnered considerable attention owing to their remarkable capabilities, leading to an increasing number of companies offering LLMs as services. Different LLMs achieve different performance at different…

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…

The nonlinear Schr\"{o}dinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate long-time simulations, particularly for multi-soliton…

We generalise the Gartner-Ellis theorem of large deviations theory. Our results allow us to derive large deviation type results in stochastic optimal control from the convergence of generalised logarithmic moment generating functions. They…

Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…

Test-Time Compute (TTC) has emerged as a powerful paradigm for enhancing the performance of Large Language Models (LLMs) at inference, leveraging strategies such as Test-Time Training (TTT) and Retrieval-Augmented Generation (RAG). However,…

Optimization modeling is fundamental to decision-making across diverse domains. Despite progress in automating optimization formulation from natural language descriptions, Large Language Models (LLMs) often struggle to generate formally…

We consider the quadratic optimization problem $\max_{x \in C}\ x^T Q x + q^T x$, where $C\subseteq\mathbb{R}^n$ is a box and $r := \mathrm{rank}(Q)$ is assumed to be $\mathcal{O}(1)$ (i.e., fixed). We show that this case can be solved in…

Existing Large Reasoning Models (LRMs) have shown the potential of reinforcement learning (RL) to enhance the complex reasoning capabilities of Large Language Models~(LLMs). While they achieve remarkable performance on challenging tasks…

Given a linear equation of the form $a_1x_1 + a_2x_2 + a_3x_3 = 0$ with integer coefficients $a_i$, we are interested in maximising the number of solutions to this equation in a set $S \subseteq \mathbb{Z}$, for sets $S$ of a given size. We…

The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and…

Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and…

In this paper, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations,…