Related papers: Defunctionalization of Higher-Order Constrained Ho…
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be…
This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by…
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
Any CNF formula can be decomposed two blocked subsets such that both can be solved by BCE (Blocked Clause Elimination). To make the decomposition more useful, one hopes to have the decomposition as unbalanced as possible. It is often time…
Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where…
The model checking problem for various fragments of first-order logic has attracted much attention over the last two decades: in particular, for the primitive positive and the positive Horn fragments, which are better known as the…
Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model…
We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Constraint Handling Rules (CHRs) are a high-level rule-based programming language for specification and implementation of constraint solvers. CHR manipulates a global store representing a flat conjunction of constraints. By default, CHR…
Hierarchical Instruction Following (HIF) refers to the problem of prompting large language models with a priority-ordered stack of instructions. Standard methods like RLHF and DPO typically fail in this problem since they mainly optimize…
We propose a categorical framework for linear-time temporal verification of effectful higher-order programs, including probabilistic higher-order programs. Our framework provides a generic denotational reduction -- namely, a denotational…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
Assume $D$ is a finite set and $R$ is a finite set of functions from $D$ to the natural numbers. An instance of the minimum $R$-cost homomorphism problem ($MinHom_R$) is a set of variables $V$ subject to specified constraints together with…
We present a Bounded Model Checking technique for higher-order programs. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to…
Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…