Journal of Symbolic Computation最新文献_第5页

D-algebraic functions D 代函数

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102377

Rida Ait El Manssour , Anna-Laura Sattelberger , Bertrand Teguia Tabuguia

引用次数: 0

Invariant neural architecture for learning term synthesis in instantiation proving 在实例化证明中学习术语合成的不变神经架构

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102375

Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota

{"title":"Invariant neural architecture for learning term synthesis in instantiation proving","authors":"Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota","doi":"10.1016/j.jsc.2024.102375","DOIUrl":"10.1016/j.jsc.2024.102375","url":null,"abstract":"<div>The development of strong CDCL-based propositional (SAT) solvers has greatly advanced several areas of automated reasoning (AR). One of the directions in AR is therefore to make use of SAT solvers in 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 synthesizing the appropriate instances from the typically infinite Herbrand universe.In this work, we develop a machine learning system targeting this task, addressing its combinatorial and invariance properties. In particular, we develop a GNN2RNN architecture based on a graph neural network (GNN) that learns from problems and their solutions independently of many symmetries and 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 combined with an efficient ground solver and, starting with zero knowledge, iteratively trained on a large corpus of mathematical problems. We show that the system is capable of solving many problems by such educated guessing, finding proofs for 32.12% of the training set. The final trained system solves 19.74% of the unseen test data on its own. We also observe that the trained system finds solutions that the iProver and CVC5 systems did not find.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102375"},"PeriodicalIF":0.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000798/pdfft?md5=03f2c9a993930436ebd44dced50d3406&pid=1-s2.0-S0747717124000798-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Graph sequence learning for premise selection 用于前提选择的图序列学习

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-27 DOI: 10.1016/j.jsc.2024.102376

Edvard K. Holden, Konstantin Korovin

引用次数: 0

Symmetric SAGE and SONC forms, exactness and quantitative gaps 对称 SAGE 和 SONC 形式、精确性和数量差距

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-13 DOI: 10.1016/j.jsc.2024.102374

Philippe Moustrou , Cordian Riener , Thorsten Theobald , Hugues Verdure

引用次数: 0

A short proof for the parameter continuation theorem 参数延续定理的简短证明

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-03 DOI: 10.1016/j.jsc.2024.102373

Viktoriia Borovik, Paul Breiding

引用次数: 0

Fast evaluation and root finding for polynomials with floating-point coefficients 浮点系数多项式的快速求值和求根

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-20 DOI: 10.1016/j.jsc.2024.102372

Rémi Imbach , Guillaume Moroz

{"title":"Fast evaluation and root finding for polynomials with floating-point coefficients","authors":"Rémi Imbach , Guillaume Moroz","doi":"10.1016/j.jsc.2024.102372","DOIUrl":"10.1016/j.jsc.2024.102372","url":null,"abstract":"<div>Evaluating or finding the roots of a polynomial <math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msup></math> with floating-point number coefficients is a ubiquitous problem. By using a piecewise approximation of f obtained with a careful use of the Newton polygon of f, we improve state-of-the-art upper bounds on the number of operations to evaluate and find the roots of a polynomial. In particular, if the coefficients of f are given with m significant bits, we provide for the first time an algorithm that finds all the roots of f with a relative condition number lower than <math><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup></math>, using a number of bit operations quasi-linear in the bit-size of the floating-point representation of f. Notably, our new approach handles efficiently polynomials with coefficients ranging from <math><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mi>d</mi></mrow></msup></math> to <math><msup><mrow><mn>2</mn></mrow><mrow><mi>d</mi></mrow></msup></math>, both in theory and in practice.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"127 ","pages":"Article 102372"},"PeriodicalIF":0.6,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computing character tables and Cartan matrices of finite monoids with fixed point counting 用定点计数计算有限单体的字符表和卡坦矩阵

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-20 DOI: 10.1016/j.jsc.2024.102371

Balthazar Charles

引用次数: 0

Signature-based standard basis algorithm under the framework of GVW algorithm GVW 算法框架下基于签名的标准基础算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-19 DOI: 10.1016/j.jsc.2024.102370

Dong Lu , Dingkang Wang , Fanghui Xiao , Xiaopeng Zheng

引用次数: 0

On symmetry adapted bases in trigonometric optimization 关于三角优化中的对称适配基

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-17 DOI: 10.1016/j.jsc.2024.102369

Tobias Metzlaff

{"title":"On symmetry adapted bases in trigonometric optimization","authors":"Tobias Metzlaff","doi":"10.1016/j.jsc.2024.102369","DOIUrl":"10.1016/j.jsc.2024.102369","url":null,"abstract":"<div>The problem of computing the global minimum of a trigonometric polynomial is computationally hard. We address this problem for the case, where the polynomial is invariant under the exponential action of a finite group. The strategy is to follow an established relaxation strategy in order to obtain a converging hierarchy of lower bounds. Those bounds are obtained by numerically solving semi-definite programs (SDPs) on the cone of positive semi-definite Hermitian Toeplitz matrices, which is outlined in the book of Dumitrescu Dumitrescu (2007). To exploit the invariance, we show that the group has an induced action on the Toeplitz matrices and prove that the feasible region of the SDP can be restricted to the invariant matrices, whilst retaining the same solution. Then we construct a symmetry adapted basis tailored to this group action, which allows us to block-diagonalize invariant matrices and thus reduce the computational complexity to solve the SDP.The approach is in its generality novel for trigonometric optimization and complements the one that was proposed as a poster at the ISSAC 2022 conference Hubert et al. (2022) and later extended to Hubert et al. (2024). In the previous work, we first used the invariance of the trigonometric polynomial to obtain a classical polynomial optimization problem on the orbit space and subsequently relaxed the problem to an SDP. Now, we first make the relaxation and then exploit invariance.Partial results of this article have been presented as a poster at the ISSAC 2023 conference Metzlaff (2023).</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"127 ","pages":"Article 102369"},"PeriodicalIF":0.6,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000737/pdfft?md5=5897477ca2a3bd75103332cdce197f3a&pid=1-s2.0-S0747717124000737-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximate GCD of several multivariate sparse polynomials based on SLRA interpolation 基于 SLRA 插值的多个多元稀疏多项式的近似 GCD

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-15 DOI: 10.1016/j.jsc.2024.102368

Kosaku Nagasaka

{"title":"Approximate GCD of several multivariate sparse polynomials based on SLRA interpolation","authors":"Kosaku Nagasaka","doi":"10.1016/j.jsc.2024.102368","DOIUrl":"10.1016/j.jsc.2024.102368","url":null,"abstract":"<div>To compute the greatest common divisor (GCD) of a set of multivariate polynomials, modular algorithms are typically employed to prevent any growth in the coefficient polynomials in the intermediate expressions. However, when dealing with multivariate polynomials with a priori errors on their coefficients, using such modular algorithms becomes challenging. This is because any resulting approximate GCD computed in one variable may have perturbations depending on the evaluation point and may not be an image of the same desired multivariate approximate GCD. This necessitates computing it as given multivariate polynomials, and operating with large matrices whose size is exponential in the number of variables. In this paper, we present a new modular algorithm, suitable for dense cases and effective for sparse ones, called “SLRA interpolation”. This algorithm uses the multidimensional fast Fourier transform (FFT) and the structured low-rank approximation (SLRA) of non-square block diagonal matrices. The SLRA interpolation technique may reduce the time-complexity for one iteration in the computation of approximate GCD of several multivariate polynomials, especially for the sparse case.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"127 ","pages":"Article 102368"},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141712328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0