Related papers: Robust Simulations and Significant Separations
The topic of provable deep neural network robustness has raised considerable interest in recent years. Most research has focused on adversarial robustness, which studies the robustness of perceptive models in the neighbourhood of particular…
This was submitted as a final project for CS254B, taught by Li Yang Tan and Tom Knowles. The field of Circuit Complexity utilises careful analysis of Boolean Circuit Functions in order to extract meaningful information about a range of…
We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…
We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the…
Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
Hybrid Communicating Sequential Processes (HCSP) is a powerful formal modeling language for hybrid systems, which is an extension of CSP by introducing differential equations for modeling continuous evolution and interrupts for modeling…
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…
We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…
With the advancement of large language models (LLMs), an increasing number of student models have leveraged LLMs to analyze textual artifacts generated by students to understand and evaluate their learning. These student models typically…
We prove an exponential separation for the sample complexity between the standard PAC-learning model and a version of the Equivalence-Query-learning model. We then show that this separation has interesting implications for adversarial…
The robustness of classifiers has become a question of paramount importance in the past few years. Indeed, it has been shown that state-of-the-art deep learning architectures can easily be fooled with imperceptible changes to their inputs.…