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Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Discrete optimisation problems arise in many different areas and are studied under many different names. In many such problems the quantity to be optimised can be expressed as a sum of functions of a restricted form. Here we present a…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
We study the existence of automatic presentations for various algebraic structures. An automatic presentation of a structure is a description of the universe of the structure by a regular set of words, and the interpretation of the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…