相关论文: The Lax-Milgram Theorem. A detailed proof to be fo…
While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides a means to formally reason about both correctness and…
We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…
Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
The Box-Cox transformation is applied to the linear mixed models for analyzing positive and grouped data. The problem in using Box Cox transformation is that the maximum likelihood estimator of the transformation parameter is generally…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
We discuss a formal framework for using algebraic structures to model a meta-language that can write, compose, and provide interoperability between abstractions of DSLs. The purpose of this formal framework is to provide a verification of…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
The power of quantum computers relies on the capability of their components to maintain faithfully and process accurately quantum information. Since this property eludes classical certification methods, fundamentally new protocols are…
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
We present a post-processing certification workflow for nonlinear elliptic boundary value problems that upgrades a standard finite element computation to a rigorous existence and output certificate. For a given approximate discrete state,…
What provides the highest level of assurance for correctness of execution within a programming language? One answer, and our solution in particular, to this problem is to provide a formalization for, if it exists, the denotational semantics…