Related papers: Robust Simulations and Significant Separations
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'',…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
We study the computational complexity of a robust version of the problem of testing two univariate C-finite functions for eventual inequality at large times. Specifically, working in the bit-model of real computation, we consider the…
This article belongs to a series on geometric complexity theory (GCT), an approach to the P vs. NP and related problems through algebraic geometry and representation theory. The basic principle behind this approach is called the flip. In…
The Split and Rephrase (SPRP) task, which consists in splitting complex sentences into a sequence of shorter grammatical sentences, while preserving the original meaning, can facilitate the processing of complex texts for humans and…
Decision making and learning in the presence of uncertainty has attracted significant attention in view of the increasing need to achieve robust and reliable operations. In the case where uncertainty stems from the presence of adversarial…
Building consistent distributed systems has largely depended on complex coordination strategies that are not only tricky to implement, but also take a toll on performance as they require nodes to wait for coordination messages. In this…
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…
Cyber-Physical Systems (CPS) in domains such as manufacturing and energy distribution generate complex time series data crucial for Prognostics and Health Management (PHM). While Deep Learning (DL) methods have demonstrated strong…
In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes $A \not= B$ especially when $A$ is known to be a subset of $B$. In this paper we…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We investigate complex self-testing, a generalization of standard self-testing that accounts for quantum strategies whose statistics is indistinguishable from their complex conjugate's. We show that many structural results from standard…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
Neural network NLP models are vulnerable to small modifications of the input that maintain the original meaning but result in a different prediction. In this paper, we focus on robustness of text classification against word substitutions,…
To develop rigorous knowledge about ML models -- and the systems in which they are embedded -- we need reliable measurements. But reliable measurement is fundamentally challenging, and touches on issues of reproducibility, scalability,…
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…
Let $\mathbb C$ be the set of complex numbers, and let $\mathcal P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P\in\mathcal P$ depends on at least two variables, we classify all possibilities for…