Related papers: A Formal Algebra for OLAP
Metadata vocabularies are used in various domains of study. It provides an in-depth description of the resources. In this work, we develop Algorithm Metadata Vocabulary (AMV), a vocabulary for capturing and storing the metadata about the…
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
The overwhelmingly increasing amount of stored data has spurred researchers seeking different methods in order to optimally take advantage of it which mostly have faced a response time problem as a result of this enormous size of data. Most…
During the last few years, a new approach to language processing has started to emerge, which has become known under various labels such as "data-oriented parsing", "corpus-based interpretation", and "tree-bank grammar" (cf. van den Berg et…
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…
In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
It is argued that transformation processes (generation rules) showing evidence of a long evolutionary history in universal computing systems can be generalized. The explicit function class $ \Omega $ is defined as follows: "Operators whose…
We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
ALAMO is a computational methodology for leaning algebraic functions from data. Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables.…
This paper introduces a new machine architecture for evaluating lambda expressions using the normal-order reduction, which guarantees that every lambda expression will be evaluated if the expression has its normal form and the system has…
Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…
Operations Research (OR) serves as a core decision-support methodology for complex systems, with significant applications across mathematics, management science, and computer science. Traditional approaches heavily rely on expert knowledge…
Model transformations are the cornerstone of Model-Driven Engineering, and provide the essential mechanisms for manipulating and transforming models. Checking whether the output of a model transformation is correct is a manual and…
Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…