3,719 research outputs found

    On the non-efficient PAC learnability of conjunctive queries

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    This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.<p/

    Cyclic proof systems for modal fixpoint logics

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    This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one

    A hybrid RBF neural network based model for day-ahead prediction of photovoltaic plant power output

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    Renewable energy resources like solar power contribute greatly to decreasing emissions of carbon dioxide and substituting generators fueled by fossil fuels. Due to the unpredictable and intermittent nature of solar power production as a result of solar radiance and other weather conditions, it is very difficult to integrate solar power into conventional power systems operation economically in a reliable manner, which would emphasize demand for accurate prediction techniques. The study proposes and applies a revised radial basis function neural network (RBFNN) scheme to predict the short-term power output of photovoltaic plant in a day-ahead prediction manner. In the proposed method, the linear as well as non-linear variables in the RBFNN scheme are efficiently trained using the whale optimization algorithm to speed the convergence of prediction results. A nonlinear benchmark function has also been used to validate the suggested scheme, which was also used in predicting the power output of solar energy for a well-designed experiment. A comparison study case generating different outcomes shows that the suggested approach could provide a higher level of prediction precision than other methods in similar scenarios, which suggests the proposed method can be used as a more suitable tool to deal such solar energy forecasting issues

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of LovĂĄsz local lemma when Δ â‰Č qᔏ. In prior, however, fast approximate counting algorithms exist when Δ â‰Č qᔏ/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. ‱ When q, k ≄ 4 are evens and Δ ≄ 5·qᔏ/ÂČ, approximating the number of hypergraph colourings is NP-hard. ‱ When the input hypergraph is linear and Δ â‰Č qᔏ/ÂČ, a fast approximate counting algorithm does exist

    Supporting the executability of R markdown files

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    R Markdown files are examples of literate programming documents that combine R code with results and explanations. Such dynamic documents are designed to execute easily and reproduce study results. However, little is known about the executability of R Markdown files which can cause frustration among its users who intend to reuse the document. This thesis aims to understand the executability of R Markdown files and improve the current state of supporting the executability of those files. Towards this direction, a large-scale study has been conducted on the executability of R Markdown files collected from GitHub repositories. Results from the study show that a significant number of R Markdown files (64.95%) are not executable, even after our best efforts. To better understand the challenges, the exceptions encountered while executing the files are categorized into different categories and a classifier is developed to determine which Markdown files are likely to be executable. Such a classifier can be utilized by search engines in their ranking which helps developers to find literate programming documents as learning resources. To support the executability of R Markdown files a command-line tool is developed. Such a tool can find issues in R Markdown files that prevent the executability of those files. Using an R Markdown file as an input, the tool generates an intuitive list of outputs that assist developers in identifying areas that require attention to ensure the executability of the file. The tool not only utilizes static analysis of source code but also uses a carefully crafted knowledge base of package dependencies to generate version constraints of involved packages and a Satisfiability Modulo Theories (SMT) solver (i.e., Z3) to identify compatible versions of those packages. Findings from this research can help developers reuse R Markdown files easily, thus improving the productivity of developers. [...

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    A Comprehensive Survey on Applications of Transformers for Deep Learning Tasks

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    Transformer is a deep neural network that employs a self-attention mechanism to comprehend the contextual relationships within sequential data. Unlike conventional neural networks or updated versions of Recurrent Neural Networks (RNNs) such as Long Short-Term Memory (LSTM), transformer models excel in handling long dependencies between input sequence elements and enable parallel processing. As a result, transformer-based models have attracted substantial interest among researchers in the field of artificial intelligence. This can be attributed to their immense potential and remarkable achievements, not only in Natural Language Processing (NLP) tasks but also in a wide range of domains, including computer vision, audio and speech processing, healthcare, and the Internet of Things (IoT). Although several survey papers have been published highlighting the transformer's contributions in specific fields, architectural differences, or performance evaluations, there is still a significant absence of a comprehensive survey paper encompassing its major applications across various domains. Therefore, we undertook the task of filling this gap by conducting an extensive survey of proposed transformer models from 2017 to 2022. Our survey encompasses the identification of the top five application domains for transformer-based models, namely: NLP, Computer Vision, Multi-Modality, Audio and Speech Processing, and Signal Processing. We analyze the impact of highly influential transformer-based models in these domains and subsequently classify them based on their respective tasks using a proposed taxonomy. Our aim is to shed light on the existing potential and future possibilities of transformers for enthusiastic researchers, thus contributing to the broader understanding of this groundbreaking technology

    Polynomial Identity Testing and the Ideal Proof System: PIT is in NP if and only if IPS can be p-simulated by a Cook-Reckhow proof system

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    The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable systems of polynomial equations. One potential drawback of IPS is that verifying an IPS proof is only known to be doable using Polynomial Identity Testing (PIT), which is solvable by a randomized algorithm, but whose derandomization, even into NSUBEXP, is equivalent to strong lower bounds. However, the circuits that are used in IPS proofs are not arbitrary, and it is conceivable that one could get around general PIT by leveraging some structure in these circuits. This proposal may be even more tempting when IPS is used as a proof system for Boolean Unsatisfiability, where the equations themselves have additional structure. Our main result is that, on the contrary, one cannot get around PIT as above: we show that IPS, even as a proof system for Boolean Unsatisfiability, can be p-simulated by a deterministically verifiable (Cook-Reckhow) proof system if and only if PIT is in NP. We use our main result to propose a potentially new approach to derandomizing PIT into NP

    Tackling Universal Properties of Minimal Trap Spaces of Boolean Networks

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    Minimal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped, whatever the update mode. They correspond to the attractors of the most permissive mode. Due to their versatility, the computation of MTSs has recently gained traction, essentially by focusing on their enumeration. In this paper, we address the logical reasoning on universal properties of MTSs in the scope of two problems: the reprogramming of Boolean networks for identifying the permanent freeze of Boolean variables that enforce a given property on all the MTSs, and the synthesis of Boolean networks from universal properties on their MTSs. Both problems reduce to solving the satisfiability of quantified propositional logic formula with 3 levels of quantifiers (∃∀∃\exists\forall\exists). In this paper, we introduce a Counter-Example Guided Refinement Abstraction (CEGAR) to efficiently solve these problems by coupling the resolution of two simpler formulas. We provide a prototype relying on Answer-Set Programming for each formula and show its tractability on a wide range of Boolean models of biological networks.Comment: Accepted at 21st International Conference on Computational Methods in Systems Biology (CMSB 2023

    When Deep Learning Meets Polyhedral Theory: A Survey

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    In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure of neural networks converged back to simpler representations based on piecewise constant and piecewise linear functions such as the Rectified Linear Unit (ReLU), which became the most commonly used type of activation function in neural networks. That made certain types of network structure \unicode{x2014}such as the typical fully-connected feedforward neural network\unicode{x2014} amenable to analysis through polyhedral theory and to the application of methodologies such as Linear Programming (LP) and Mixed-Integer Linear Programming (MILP) for a variety of purposes. In this paper, we survey the main topics emerging from this fast-paced area of work, which bring a fresh perspective to understanding neural networks in more detail as well as to applying linear optimization techniques to train, verify, and reduce the size of such networks
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