Related papers: A Formal Algebra for OLAP
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
Multidimensional Big Data Analytics is an emerging area that marries the capabilities of OLAP with modern Big Data Analytics. Essentially, the idea is engrafting multidimensional models into Big Data analytics processes to gain into…
We report on implementing graph grammars for intelligence analysis in OCaml. Graph grammars are represented as elements of an algebraic data type in OCaml. In addition to algebraic data types, we use other concepts from functional…
On line analytical processing (OLAP) is an essential element of decision-support systems. OLAP tools provide insights and understanding needed for improved decision making. However, the answers to OLAP queries can be biased and lead to…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
Large amounts of spatial, textual, and temporal data are being produced daily. This is data containing an unstructured component (text), a spatial component (geographic position), and a time component (timestamp). Therefore, there is a need…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
The execution logs that are used for process mining in practice are often obtained by querying an operational database and storing the result in a flat file. Consequently, the data processing power of the database system cannot be used…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional Multidimensional in data warehouse is a compulsion and become the most important for information delivery,…
Object-Oriented Programming (OOP) has become a crucial paradigm for managing the growing complexity of modern software systems, particularly in fields like machine learning, deep learning, large language models (LLM), and data analytics.…
The meet up between data, processes and structural knowledge in modeling enterprise systems is a challenging task that has led to the study of combining formalisms from knowledge representation, database theory, and process management. To…
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…