Graph Sequence Learning for Premise Selection

Premise selection is crucial for large theory reasoning as the sheer size of the problems quickly leads to resource starvation. This paper proposes a premise selection approach inspired by the domain of image captioning, where language models automatically generate a suitable caption for a given image. Likewise, we attempt to generate the sequence of axioms required to construct the proof of a given problem. This is achieved by combining a pre-trained graph neural network with a language model. We evaluated different configurations of our method and experience a 17.7% improvement gain over the baseline.Comment: 17 page

Machine Learning Meets The Herbrand Universe

The appearance of strong CDCL-based propositional (SAT) solvers has greatly advanced several areas of automated reasoning (AR). One of the directions in AR is thus to apply SAT solvers to expressive formalisms such as first-order logic, for which large corpora of general mathematical problems exist today. This is possible due to Herbrand's theorem, which allows reduction of first-order problems to propositional problems by instantiation. The core challenge is choosing the right instances from the typically infinite Herbrand universe. In this work, we develop the first machine learning system targeting this task, addressing its combinatorial and invariance properties. In particular, we develop a GNN2RNN architecture based on an invariant graph neural network (GNN) that learns from problems and their solutions independently of symbol names (addressing the abundance of skolems), combined with a recurrent neural network (RNN) that proposes for each clause its instantiations. The architecture is then trained on a corpus of mathematical problems and their instantiation-based proofs, and its performance is evaluated in several ways. We show that the trained system achieves high accuracy in predicting the right instances, and that it is capable of solving many problems by educated guessing when combined with a ground solver. To our knowledge, this is the first convincing use of machine learning in synthesizing relevant elements from arbitrary Herbrand universes.Comment: 8 pages, 10 figure

LGEM+^\text{+}: a first-order logic framework for automated improvement of metabolic network models through abduction

Scientific discovery in biology is difficult due to the complexity of the systems involved and the expense of obtaining high quality experimental data. Automated techniques are a promising way to make scientific discoveries at the scale and pace required to model large biological systems. A key problem for 21st century biology is to build a computational model of the eukaryotic cell. The yeast Saccharomyces cerevisiae is the best understood eukaryote, and genome-scale metabolic models (GEMs) are rich sources of background knowledge that we can use as a basis for automated inference and investigation. We present LGEM+, a system for automated abductive improvement of GEMs consisting of: a compartmentalised first-order logic framework for describing biochemical pathways (using curated GEMs as the expert knowledge source); and a two-stage hypothesis abduction procedure. We demonstrate that deductive inference on logical theories created using LGEM+, using the automated theorem prover iProver, can predict growth/no-growth of S. cerevisiae strains in minimal media. LGEM+ proposed 2094 unique candidate hypotheses for model improvement. We assess the value of the generated hypotheses using two criteria: (a) genome-wide single-gene essentiality prediction, and (b) constraint of flux-balance analysis (FBA) simulations. For (b) we developed an algorithm to integrate FBA with the logic model. We rank and filter the hypotheses using these assessments. We intend to test these hypotheses using the robot scientist Genesis, which is based around chemostat cultivation and high-throughput metabolomics.Comment: 15 pages, one figure, two tables, two algorithm

Computing exponentially faster: Implementing a nondeterministic universal Turing machine using DNA

The theory of computer science is based around Universal Turing Machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of UTMs. The nondeterministic polynomial (NP) time complexity class of problems is the most significant in computer science, and an efficient (i.e. polynomial P) way to solve such problems would be of profound economic and social importance. By definition nondeterministic UTMs (NUTMs) solve NP complete problems in P time. However, NUTMs have previously been believed to be physically impossible to construct. Thue string rewriting systems are computationally equivalent to UTMs, and are naturally nondeterministic. Here we describe the physical design for a NUTM that implements a universal Thue system. The design exploits the ability of DNA to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that this design works using both computational modelling and in vitro molecular biology experimentation. The current design has limitations, such as restricted error-correction. However, it opens up the prospect of engineering NUTM based computers able to outperform all standard computers on important practical problems

Создание кольцевой антенной решетки на основе излучателей Вивальди для широкополосного канала связи с ретрансляцией

Introduction. Unmanned aerial vehicles (UAVs) are rapidly gaining in popularity. The UVA development requires active antenna systems capable of forming a narrow beam of the main lobe of the radiation pattern. Although numerous studies have considered specialized antenna arrays with a wide range of scanning angles, the location of such systems on UAVs remains under-investigated. The development of such arrays for UAVs will enable the creation of a secure relay broadband channel with a few repeaters.Aim. Development of a broadband antenna array for UAVs with the possibility of setting the main lobe of the radiation pattern in any direction of the azimuthal plane, for use in relay tasks.Materials and methods. An emitter model and a circular antenna array on its basis was developed in the Ansys HFSS electromagnetic modeling package.Results. The dependence of the directional coefficient and the gain for an array consisting of 8 and 16 elements was shown. Voltage standing-wave ratio dependences and directivity patterns that satisfy the conditions of retransmission in a wide-frequency band using UAVs were obtained. Recommendations on the number of active elements in a circular antenna array that ensure the maximum gain (directivity) were formulated.Conclusion. Technical solutions that can be used in the development of UAVs are proposed. The system can be further improved by optimizing the antenna array elements and using a cylindrical or hemispherical array.Введение. В настоящее время беспилотные летательные аппараты (БПЛА) находят все более широкое применение. Одной из задач развития БПЛА является создание активных антенных систем с возможностью установки узкого луча главного лепестка диаграммы направленности (ДН). Несмотря на то, что во многих исследованиях рассматривается создание специализированных антенных решеток с широким диапазоном углов сканирования, особенности расположения таких систем на БПЛА не изучались подробно. После разработки таких решеток для БПЛА возможно создание цепи ретрансляции с защищенным широкополосным каналом.Цель работы. Разработка широкополосной антенной системы для БПЛА с возможностью установки главного лепестка ДН в любом направлении азимутальной плоскости для использования в задачах ретрансляции.Материалы и методы. В рамках исследования разработана модель излучателя и кольцевой антенной решетки на его основе в пакете электромагнитного моделирования Ansys HFSS.Результаты. Показаны частотные зависимости коэффициента направленного действия (КНД) и коэффициента усиления (КУ) для кольцевой антенной решетки, состоящей из 8 и 16 элементов, а также частотные зависимости коэффициента стоячей волны по напряжению и ДН, удовлетворяющие условиям ретрансляции в широкой полосе частот с использованием БПЛА. Представлены рекомендации по количеству активных элементов кольцевой решетки для обеспечения максимума КУ (КНД).Заключение. Предложены конструктивные решения для использования антенных систем на БПЛА. В дальнейшем система может быть улучшена за счет оптимизации элементов антенной решетки и использования цилиндрической или полусферической решетки