scholarly journals Initial Experiments on Deriving a Complete HOL Simplification Set

10.29007/95qb ◽  
2018 ◽  
Author(s):  
Cezary Kaliszyk ◽  
Thomas Sternagel
Keyword(s):  
State Of The Art ◽  
Desirable Property ◽  
Proof Assistant ◽  
Proof Assistants ◽  
First Order

Rewriting is a common functionality in proof assistants, that allows to simplify theorems and goals. The set of equations to use in a rewrite step has to be manually specified, and therefore often includes rules which may lead to non-termination. Even in the case of termination another desirable property of a simplification set would be confluence. A well-known technique from rewriting to transform a terminating system into a terminating and confluent one is completion. But the sets of equations we find in the context of proof assistants are typically huge and most state-of-the-art completion tools only work on relatively small problems. In this paper we describe our initial experiments with the aim to close the gap and use rewriting to compute a complete first-order simplification set for a HOL-based proof assistant fully automatically.

scholarly journals Efficient Graph Collaborative Filtering via Contrastive Learning

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4666
Author(s):  
Zhiqiang Pan ◽  
Honghui Chen
Keyword(s):  
Collaborative Filtering ◽  
State Of The Art ◽  
Representation Learning ◽  
First Order ◽  
Satisfactory Performance ◽  
Potential Applications ◽  
Benchmark Datasets ◽  
Bayesian Personalized Ranking ◽  
Graph Neural Networks ◽  
Training Efficiency

Collaborative filtering (CF) aims to make recommendations for users by detecting user’s preference from the historical user–item interactions. Existing graph neural networks (GNN) based methods achieve satisfactory performance by exploiting the high-order connectivity between users and items, however they suffer from the poor training efficiency problem and easily introduce bias for information propagation. Moreover, the widely applied Bayesian personalized ranking (BPR) loss is insufficient to provide supervision signals for training due to the extremely sparse observed interactions. To deal with the above issues, we propose the Efficient Graph Collaborative Filtering (EGCF) method. Specifically, EGCF adopts merely one-layer graph convolution to model the collaborative signal for users and items from the first-order neighbors in the user–item interactions. Moreover, we introduce contrastive learning to enhance the representation learning of users and items by deriving the self-supervisions, which is jointly trained with the supervised learning. Extensive experiments are conducted on two benchmark datasets, i.e., Yelp2018 and Amazon-book, and the experimental results demonstrate that EGCF can achieve the state-of-the-art performance in terms of Recall and normalized discounted cumulative gain (NDCG), especially on ranking the target items at right positions. In addition, EGCF shows obvious advantages in the training efficiency compared with the competitive baselines, making it practicable for potential applications.

scholarly journals A secure and highly efficient first-order masking scheme for AES linear operations

Cybersecurity ◽  
2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jingdian Ming ◽  
Yongbin Zhou ◽  
Huizhong Li ◽  
Qian Zhang
Keyword(s):  
Cost Reduction ◽  
Provable Security ◽  
State Of The Art ◽  
Side Channel ◽  
First Order ◽  
Highly Efficient ◽  
Non Linear ◽  
Device Independence ◽  
Practical Implications ◽  
Provably Secure

AbstractDue to its provable security and remarkable device-independence, masking has been widely accepted as a noteworthy algorithmic-level countermeasure against side-channel attacks. However, relatively high cost of masking severely limits its applicability. Considering the high tackling complexity of non-linear operations, most masked AES implementations focus on the security and cost reduction of masked S-boxes. In this paper, we focus on linear operations, which seems to be underestimated, on the contrary. Specifically, we discover some security flaws and redundant processes in popular first-order masked AES linear operations, and pinpoint the underlying root causes. Then we propose a provably secure and highly efficient masking scheme for AES linear operations. In order to show its practical implications, we replace the linear operations of state-of-the-art first-order AES masking schemes with our proposal, while keeping their original non-linear operations unchanged. We implement four newly combined masking schemes on an Intel Core i7-4790 CPU, and the results show they are roughly 20% faster than those original ones. Then we select one masked implementation named RSMv2 due to its popularity, and investigate its security and efficiency on an AVR ATMega163 processor and four different FPGA devices. The results show that no exploitable first-order side-channel leakages are detected. Moreover, compared with original masked AES implementations, our combined approach is nearly 25% faster on the AVR processor, and at least 70% more efficient on four FPGA devices.

scholarly journals CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

2011 ◽  
Vol 21 (4) ◽  
pp. 827-859 ◽  
Author(s):  
FRÉDÉRIC BLANQUI ◽  
ADAM KOPROWSKI
Keyword(s):  
Term Rewriting ◽  
Automated Verification ◽  
Proof Assistant ◽  
Proof Assistants ◽  
Active Subject ◽  
Turing Complete

Termination is an important property of programs, and is notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting. Over the years, many methods and tools have been developed to address the problem of deciding termination for specific problems (since it is undecidable in general). Ensuring the reliability of those tools is therefore an important issue.In this paper we present a library formalising important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools.The sources are freely available athttp://color.inria.fr/.

Formalization of metatheory of the Lambda Calculus in constructive type theory using the Barendregt variable convention

2021 ◽  
pp. 1-20
Author(s):  
Ernesto Copello ◽  
Nora Szasz ◽  
Álvaro Tasistro
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Proof Assistant ◽  
First Order ◽  
Constructive Type Theory ◽  
Fundamental Part ◽  
Constructive Type ◽  
Free Variables ◽  
The Church ◽  
Theoretical Results

Abstarct We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.

Sparse Convex Regression

2020 ◽  
Author(s):  
Dimitris Bertsimas ◽  
Nishanth Mundru
Keyword(s):  
Least Squares ◽  
State Of The Art ◽  
Cutting Plane ◽  
Cutting Plane Method ◽  
Cutting Plane Methods ◽  
Regression Problem ◽  
Scalable Algorithm ◽  
First Order ◽  
False Discovery ◽  
Convex Regression

We consider the problem of best [Formula: see text]-subset convex regression using [Formula: see text] observations in [Formula: see text] variables. For the case without sparsity, we develop a scalable algorithm for obtaining high quality solutions in practical times that compare favorably with other state of the art methods. We show that by using a cutting plane method, the least squares convex regression problem can be solved for sizes [Formula: see text] in minutes and [Formula: see text] in hours. Our algorithm can be adapted to solve variants such as finding the best convex or concave functions with coordinate-wise monotonicity, norm-bounded subgradients, and minimize the [Formula: see text] loss—all with similar scalability to the least squares convex regression problem. Under sparsity, we propose algorithms which iteratively solve for the best subset of features based on first order and cutting plane methods. We show that our methods scale for sizes [Formula: see text] in minutes and [Formula: see text] in hours. We demonstrate that these methods control for the false discovery rate effectively.

scholarly journals Enhanced Knowledge Graph Embedding by Jointly Learning Soft Rules and Facts

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 265 ◽  
Author(s):  
Jindou Zhang ◽  
Jing Li
Keyword(s):  
Link Prediction ◽  
State Of The Art ◽  
Background Knowledge ◽  
Background Information ◽  
Knowledge Graph ◽  
Logical Inference ◽  
Training Algorithm ◽  
First Order ◽  
Forward Chaining ◽  
Logical Rules

Combining first order logic rules with a Knowledge Graph (KG) embedding model has recently gained increasing attention, as rules introduce rich background information. Among such studies, models equipped with soft rules, which are extracted with certain confidences, achieve state-of-the-art performance. However, the existing methods either cannot support the transitivity and composition rules or take soft rules as regularization terms to constrain derived facts, which is incapable of encoding the logical background knowledge about facts contained in soft rules. In addition, previous works performed one time logical inference over rules to generate valid groundings for modeling rules, ignoring forward chaining inference, which can further generate more valid groundings to better model rules. To these ends, this paper proposes Soft Logical rules enhanced Embedding (SoLE), a novel KG embedding model equipped with a joint training algorithm over soft rules and KG facts to inject the logical background knowledge of rules into embeddings, as well as forward chaining inference over rules. Evaluations on Freebase and DBpedia show that SoLE not only achieves improvements of 11.6%/5.9% in Mean Reciprocal Rank (MRR) and 18.4%/15.9% in HITS@1 compared to the model on which SoLE is based, but also significantly and consistently outperforms the state-of-the-art baselines in the link prediction task.

scholarly journals Towards closed world reasoning in dynamic open worlds

2010 ◽  
Vol 10 (4-6) ◽  
pp. 547-563 ◽  
Author(s):  
MARTIN SLOTA ◽  
JOÃO LEITE
Keyword(s):  
Semantic Web ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Static Case ◽  
First Order ◽  
Closed World ◽  
Hybrid Knowledge ◽  
First Time

AbstractThe need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics forhybrid knowledge basescomposed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve.In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties.To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

Company News

2001 ◽  
Vol 05 (14) ◽  
pp. 291-301
Keyword(s):  
Medical Devices ◽  
Strategic Alliance ◽  
State Of The Art ◽  
Life Sciences ◽  
Medical Products ◽  
First Order ◽  
Commercial Use ◽  
Sign Distribution ◽  
Wastewater Recycling ◽  
Set Up

Cell Robotics' Medical Devices Well Received in China. US National Nutritional Foods Association and China's Sanjiu Pharmaceutical Establish Historic Partnership. Novacor LVAS Approved for Commercial Use in Japan. NOMOS and Lynmed to Jointly Distribute Medical Products in China and HK. Eli Lilly to Buy Out Ranbaxy's Stake. US-based Dragon Expands Business in Hong Kong and China. Australia's Global Doctor and US MedAire Announce Strategic Alliance. Taiwan's Gene Born Biotech Corp Adopts Thermogenesis's BioArchive System. Cepheid and BioSynTech Sign Distribution Agreement To Enter Life Sciences Research Market in Southeast Asia. Harbin Pharmaceutical Completes China's Largest Antibiotic Wastewater Recycling Project. Eli Lilly to Set Up State-of-the-Art Systems Biology R&D Center in Singapore. Varian Receives First Order for World's Most Powerful NMR Spectrometer from Japan.

scholarly journals Competitive Proving for Fun

10.29007/ktx8 ◽  
2019 ◽  
Author(s):  
Maximilian Paul Louis Haslbeck ◽  
Simon Wimmer
Keyword(s):  
Theorem Proving ◽  
System Architecture ◽  
Large Scale ◽  
Research Field ◽  
Proof Assistant ◽  
Proof Assistants ◽  
Prototype Implementation ◽  
New Generation

We propose a system for large-scale theorem proving contests. We hope that such contests could spark interest in the research field, attract a new generation of theorem proving savants, and foster competition among proof assistants. For the proof assistant Isabelle, we construct and evaluate two iterations of a prototype implementation of our proposed system architecture.

scholarly journals Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1623
Author(s):  
Jie Chen ◽  
Ryosuke Shimmura ◽  
Joe Suzuki
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
High Accuracy ◽  
Alternating Direction Method ◽  
Main Approach ◽  
First Order ◽  
Gradient Algorithms ◽  
Graphical Lasso ◽  
Alternating Direction ◽  
Accuracy And Precision

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

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