Related papers: Enumeration and updates for conjunctive linear alg…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the…
Many analytics tasks and machine learning problems can be naturally expressed by iterative linear algebra programs. In this paper, we study the incremental view maintenance problem for such complex analytical queries. We develop a…
Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation…
We study the fine-grained complexity of conjunctive queries with grouping and aggregation. For common aggregate functions (e.g., min, max, count, sum), such a query can be phrased as an ordinary conjunctive query over a database annotated…
As data analytics becomes more crucial to digital systems, so grows the importance of characterizing the database queries that admit a more efficient evaluation. We consider the tractability yardstick of answer enumeration with a…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over…
Quantum kernels are considered as potential resources to illustrate benefits of quantum computing in machine learning. Considering the impact of hyperparameters on the performance of a classical machine learning model, it is imperative to…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
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…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
The article studies query evaluation in parallel constant time in the CRCW PRAM model. While it is well-known that all relational algebra queries can be evaluated in constant time on an appropriate CRCW PRAM model, this article is…
We study how to evaluate MSO queries with free variables on trees, within the framework of enumeration algorithms. Previous work has shown how to enumerate answers with linear-time preprocessing and delay linear in the size of each output,…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
Linear algebra operations, which are ubiquitous in machine learning, form major performance bottlenecks. The High-Performance Computing community invests significant effort in the development of architecture-specific optimized kernels, such…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced…