Related papers: Descriptive Complexity of $\#\textrm{AC}^0$ Functi…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a…
Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock…
Intrinsic complexity of a relation on a given computable structure is captured by the notion of its degree spectrum - the set of Turing degrees of images of the relation in all computable isomorphic copies of that structure. We investigate…
Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
Descriptive complexity may be useful to design programs in a natural declarative way. This is important for parallel computation models such as cellular automata, because designing parallel programs is considered difficult. Our paper…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
This introduction to arithmetic coding is divided in two parts. The first explains how and why arithmetic coding works. We start presenting it in very general terms, so that its simplicity is not lost under layers of implementation details.…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…