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DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…
Domain specific languages have successfully been used in a variety of fields to cleanly express scientific problems as well as to simplify implementation and performance opti- mization on different computer architectures. Although a large…
In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recursions, enabling it to solve large-scale algebraic Riccati…
In offline reinforcement learning, value overestimation caused by out-of-distribution (OOD) actions significantly limits policy performance. Recently, diffusion models have been leveraged for their strong distribution-matching capabilities,…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Regular expressions are widely used in software. Various regular expression engines support different combinations of extensions to classical regular constructs such as Kleene star, concatenation, nondeterministic choice (union in terms of…
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We take an algorithmic and computational approach to a basic problem in abstract algebra: determining the correct generalization to dialgebras of a given variety of nonassociative algebras. We give a simplified statement of the KP algorithm…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Double Boolean algebras (dBas), introduced by Wille, are based on twenty-three identities. We present a simplified axiom system, the D-core algebra, and prove it is equivalent to Wille's original definition. This reduction allows improved…
We investigate the complexity of evaluating queries in Relational Algebra (RA) over the relations extracted by regex formulas (i.e., regular expressions with capture variables) over text documents. Such queries, also known as the regular…
We present a formal study of semantics for the relational programming language miniKanren. First, we formulate a denotational semantics which corresponds to the minimal Herbrand model for definite logic programs. Second, we present…
Document-level relation extraction (DocRE) involves identifying relations between entities distributed in multiple sentences within a document. Existing methods focus on building a heterogeneous document graph to model the internal…
Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss,…
We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (2013). Our definition uses a construction…
We present a new QCD evolution library for unpolarized parton distribution functions: EKO. The program solves DGLAP equations up to next-to-next-to-leading order. The unique feature of EKO is the computation of solution operators, which are…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling…
Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined…