Related papers: From Numbers to Container Strings
We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…
Batch codes, introduced by Ishai et al. encode a string $x \in \Sigma^{k}$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each…
Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…
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…
Factorization of string amplitudes is one way of constructing string interaction vertices. We show that correlation functions in string theory can be conveniently factorized using loop variables representing delta functionals. We illustrate…
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…
In the deletion channel, an important problem is to determine the number of subsequences derived from a string $U$ of length $n$ when subjected to $t$ deletions. It is well-known that the number of subsequences in the setting exhibits a…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly,…
In this short note, we show a simple characterization of integers that reach records for a sequence described by adding binary strings to runs of 1's and 0's in a binary representation. In particular, we show that this set does not depend…
Ranking theories according to their strength is a recurring motif in mathematical logic. We introduce a new ranking of arbitrary (not necessarily recursively axiomatized) theories in terms of the encoding power of their $\beta$-models:…
This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the…
We describe an attentive encoder that combines tree-structured recursive neural networks and sequential recurrent neural networks for modelling sentence pairs. Since existing attentive models exert attention on the sequential structure, we…
We derive a class of solutions to the string sigma-model equations for the closed bosonic string. The tachyon field is taken to form a constant condensate and the beta-function equations at one-loop level are solved for the evolution of the…
We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off-shell) level-matched closed string states are represented by star algebra projectors in open…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
Widespread use of string solvers in formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an…