Related papers: Associative string functions
An alternating colouring function is defined on strings over the alphabet $\{0, 1\}$. It divides the strings in colourable and non-colourable ones. The points in the subshift of finite type defined by forbidding all non-colourable strings…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
It is argued that string theory may pose new conceptual issues for the history and philosophy of science.
As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require…
String Theory is a hot topic of physics and mathematics. For the former, it stands as a huge sandbox where the formulation of difficult problems can be simplified and their hard computations carried out. For the latter, it stands as a…
Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent,…
In this paper we propose a new, more appropriate definition of regular and indeterminate strings. A regular string is one that is "isomorphic" to a string whose entries all consist of a single letter, but which nevertheless may itself…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…
We introduce a string-interval abstract domain, where string intervals are characterized by systems of word equations (encoding lower bounds on string values) and word disequalities (encoding upper bounds). Building upon the lattice…
Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are…
String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor…