6,189 research outputs found

    Undergraduate Catalog of Studies, 2023-2024

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    A foundation for synthesising programming language semantics

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    Programming or scripting languages used in real-world systems are seldom designed with a formal semantics in mind from the outset. Therefore, the first step for developing well-founded analysis tools for these systems is to reverse-engineer a formal semantics. This can take months or years of effort. Could we automate this process, at least partially? Though desirable, automatically reverse-engineering semantics rules from an implementation is very challenging, as found by Krishnamurthi, Lerner and Elberty. They propose automatically learning desugaring translation rules, mapping the language whose semantics we seek to a simplified, core version, whose semantics are much easier to write. The present thesis contains an analysis of their challenge, as well as the first steps towards a solution. Scaling methods with the size of the language is very difficult due to state space explosion, so this thesis proposes an incremental approach to learning the translation rules. I present a formalisation that both clarifies the informal description of the challenge by Krishnamurthi et al, and re-formulates the problem, shifting the focus to the conditions for incremental learning. The central definition of the new formalisation is the desugaring extension problem, i.e. extending a set of established translation rules by synthesising new ones. In a synthesis algorithm, the choice of search space is important and non-trivial, as it needs to strike a good balance between expressiveness and efficiency. The rest of the thesis focuses on defining search spaces for translation rules via typing rules. Two prerequisites are required for comparing search spaces. The first is a series of benchmarks, a set of source and target languages equipped with intended translation rules between them. The second is an enumerative synthesis algorithm for efficiently enumerating typed programs. I show how algebraic enumeration techniques can be applied to enumerating well-typed translation rules, and discuss the properties expected from a type system for ensuring that typed programs be efficiently enumerable. The thesis presents and empirically evaluates two search spaces. A baseline search space yields the first practical solution to the challenge. The second search space is based on a natural heuristic for translation rules, limiting the usage of variables so that they are used exactly once. I present a linear type system designed to efficiently enumerate translation rules, where this heuristic is enforced. Through informal analysis and empirical comparison to the baseline, I then show that using linear types can speed up the synthesis of translation rules by an order of magnitude

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Multidisciplinary perspectives on Artificial Intelligence and the law

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    This open access book presents an interdisciplinary, multi-authored, edited collection of chapters on Artificial Intelligence (‘AI’) and the Law. AI technology has come to play a central role in the modern data economy. Through a combination of increased computing power, the growing availability of data and the advancement of algorithms, AI has now become an umbrella term for some of the most transformational technological breakthroughs of this age. The importance of AI stems from both the opportunities that it offers and the challenges that it entails. While AI applications hold the promise of economic growth and efficiency gains, they also create significant risks and uncertainty. The potential and perils of AI have thus come to dominate modern discussions of technology and ethics – and although AI was initially allowed to largely develop without guidelines or rules, few would deny that the law is set to play a fundamental role in shaping the future of AI. As the debate over AI is far from over, the need for rigorous analysis has never been greater. This book thus brings together contributors from different fields and backgrounds to explore how the law might provide answers to some of the most pressing questions raised by AI. An outcome of the Católica Research Centre for the Future of Law and its interdisciplinary working group on Law and Artificial Intelligence, it includes contributions by leading scholars in the fields of technology, ethics and the law.info:eu-repo/semantics/publishedVersio

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    UMSL Bulletin 2022-2023

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    The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp

    Witnessing environment dimension through temporal correlations

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    We introduce a framework to compute upper bounds for temporal correlations achievable in open quantum system dynamics, obtained by repeated measurements on the system. As these correlations arise by virtue of the environment acting as a memory resource, such bounds are witnesses for the minimal dimension of an effective environment compatible with the observed statistics. These witnesses are derived from a hierarchy of semidefinite programs with guaranteed asymptotic convergence. We compute non-trivial bounds for various sequences involving a qubit system and a qubit environment, and compare the results to the best known quantum strategies producing the same outcome sequences. Our results provide a numerically tractable method to determine bounds on multi-time probability distributions in open quantum system dynamics and allow for the witnessing of effective environment dimensions through probing of the system alone.Comment: 24 pages, 7 figure
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