Related papers: Creating a dynamic database of finite groups
Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of…
A common approach to data analysis involves understanding and manipulating succinct representations of data. In earlier work, we put forward a succinct representation system for relational data called factorised databases and reported on…
We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by…
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to…
Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures…
Halls of Fame are fascinating constructs. They represent the elite of an often very large amount of entities---persons, companies, products, countries etc. Beyond their practical use as static rankings, changes to them are particularly…
Generating an abstraction of a dynamic domain that aligns with a given purpose remains a significant challenge given that the choice of such an abstraction can impact an agent's ability to plan, reason, and provide explanations effectively.…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Translating continuous control system models into finite automata allows us to use powerful discrete tools to synthesize controllers for complex specifications. The abstraction construction step is unfortunately hamstrung by high runtime…
Many databases on the web are "hidden" behind (i.e., accessible only through) their restrictive, form-like, search interfaces. Recent studies have shown that it is possible to estimate aggregate query answers over such hidden web databases…
Graph databases have become essential tools for managing complex and interconnected data, which is common in areas like social networks, bioinformatics, and recommendation systems. Unlike traditional relational databases, graph databases…
The demanding requirements of the new Big Data intensive era raised the need for flexible storage systems capable of handling huge volumes of unstructured data and of tackling the challenges that traditional databases were facing. NoSQL…
Tables form a central component in both exploratory data analysis and formal reporting procedures across many industries. These tables are often complex in their conceptual structure and in the computations that generate their individual…
We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings…
Document databases are increasingly popular in various applications, but their queries are challenging to write due to the flexible and complex data model underlying document databases. This paper presents a synthesis technique that aims to…
As we embark on a new era of LLMs, it becomes increasingly crucial to understand their capabilities, limitations, and differences. Toward making further progress in this direction, we strive to build a deeper understanding of the gaps…
We propose a new approach to querying graph databases. Our approach balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
The automated synthesis of control policies for stochastic dynamical systems presents significant challenges. A standard approach is to construct a finite-state abstraction of the continuous system, typically represented as a Markov…
Let $R$ be a ring, let $G$ be an amenable group and let $R\ast G$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function $L$ on the category of left modules over $R$, an additive function on…