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This paper presents a computationally-efficient method for evaluating the feasibility of Quadratic Programs (QPs) for online constrained control. Based on the duality principle, we first show that the feasibility of a QP can be determined…

Quantifier elimination (qelim) is used in many automated reasoning tasks including program synthesis, exist-forall solving, quantified SMT, Model Checking, and solving Constrained Horn Clauses (CHCs). Exact qelim is computationally…

Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming…

In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…

Fluid models provide a tractable approach to approximate multiclass processing networks. This tractability is a due to the fact that optimal control for such models is a solution of a Separated Continuous Linear Programming (SCLP) problem.…

Conditional validity and length efficiency are two crucial aspects of conformal prediction (CP). Conditional validity ensures accurate uncertainty quantification for data subpopulations, while proper length efficiency ensures that the…

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across…

We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…

It is imperative for Large language models (LLMs) to follow instructions with elaborate requirements (i.e. Complex Instructions Following). Yet, it remains under-explored how to enhance the ability of LLMs to follow complex instructions…

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial…

Large Language Models (LLMs) have demonstrated remarkable ability in long-horizon Task and Motion Planning (TAMP) by translating clear and straightforward natural language problems into formal specifications such as the Planning Domain…

Large language models (LLMs) have garnered increasing attention owing to their powerful logical reasoning capabilities. Generally, larger LLMs (L-LLMs) that require paid interfaces exhibit significantly superior performance compared to…

The main goal of this master's thesis is to introduce Quantum Natural Language Processing (QNLP) in a way understandable by both the NLP engineer and the quantum computing practitioner. QNLP is a recent application of quantum computing that…

Fine-grained skill representations, commonly referred to as knowledge components (KCs), are fundamental to many approaches in student modeling and learning analytics. However, KC-level correctness labels are rarely available in real-world…

Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…

Pre-trained language models (PLMs) have been prevailing in state-of-the-art methods for natural language processing, and knowledge-enhanced PLMs are further proposed to promote model performance in knowledge-intensive tasks. However,…

Although large language models (LLMs) show promising potential in code translation, they still struggle to generate accurate translations using the commonly adopted direct code-to-code translation approach, which converts an original…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…