Related papers: On the complexity of finite valued functions
In this paper we present a new class of complexity measures, induced by a new data structure for representing $k$-valued functions (operations), called minor decision diagram. The results are presented in terms of Multi-Valued Logic…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…
We consider various definitions of degrees of discrete functions and establish relations between the number of relevant (essential) variables and degrees of two- and three-valued functions. Keywords: relevant variable, sensitivity, degree…
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,…
Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. We particularly solve a problem concerning the…
Infamously, the finite and unrestricted implication problems for the classes of i) functional and inclusion dependencies together, and ii) embedded multivalued dependencies alone are each undecidable. Famously, the restriction of i) to…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first of all the Bessel functions of first…
In a recent article, we introduced and studied a precise class of dynamical systems called solvable systems. These systems present a dynamic ruled by discontinuous ordinary differential equations with solvable right-hand terms and unique…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to non-empty compact subsets of $\mathbb{R}^d$, $F: [a,b] \to K(\mathbb{R}^d)$, we discuss the problem of computing good approximations of F. We…
Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…