Related papers: Separation Results for Boolean Function Classes
Difference sets are subsets of a group satisfying certain combinatorial property with respect to the group operation. They can be characterized using an equality in the group ring of the corresponding group. In this paper, we exploit the…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
We investigate the polynomial closure operation (C -> Pol(C)) defined on classes of regular languages. We present an interesting and useful connection relating the separation problem for the class C and the membership problem for it…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
Many different programs are the implementation of the same algorithm. The collection of programs can be partitioned into different classes corresponding to the algorithms they implement. This makes the collection of algorithms a quotient of…
Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…
The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis…
Linear classifier probes are frequently utilized to better understand how neural networks function. Researchers have approached the problem of determining unit importance in neural networks by probing their learned, internal…
Let A be a finite set with at least two elements. The composition of two classes I and J of operations on A, is defined as the set of all compositions of functions in I with functions in J. This binary operation gives a monoid structure to…
In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular,…