Related papers: A Complexity Theory for Hard Enumeration Problems
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
The determination of environmentally- and economically-optimal energy system designs and operations is complex. In particular, the integration of weather-dependent renewable energy technologies into energy system optimization models…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
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…
In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and…
Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…
Training a Neural Network (NN) with lots of parameters or intricate architectures creates undesired phenomena that complicate the optimization process. To address this issue we propose a first modular approach to NN design, wherein the NN…
Spreadsheets are widely used in industry, even for critical business processes. This implies the need for proper risk assessment in spreadsheets to evaluate the reliability and validity of the spreadsheet's outcome. As related research has…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
We often add arithmetic to extend the expressiveness of query languages and study the complexity of problems such as testing query containment and finding certain answers in the framework of answering queries using views. When adding…
Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
We study complexity of the index set of countably categorical theories and Ehrenfeucht theories in finite languages.
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…