Related papers: Associative string functions
We investigate the associativity property for functions of indefinite arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.
We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some consequences of this…
The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
The distance of an operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Associative spectra were introduced in a publication by B. Cs\'ak\'any and T. Waldhauser in…
We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
String constraint solving refers to solving combinatorial problems involving constraints over string variables. String solving approaches have become popular over the last years given the massive use of strings in different application…
Every partial function from bit strings of a given length to bit strings of a possibly different given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers,…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as…
This is the written version of a set of introductory lectures on string theory.