发帖
雷达卡
摘要翻译：
本文提出了一种人工智能技术&爬山法来求解丢番图方程的数值解。这类方程在公钥密码学、整数分解、代数曲线、射影曲线和超级计算机中的数据依赖等领域有着重要的应用。重要的是，已经证明没有一般的方法来求这类方程的解。本文试图用爬山的最速上升形式求丢番图方程的数值解。该方法利用树表示来描述丢番图方程的可能解，并采用一种新的方法来生成后继子。启发式函数使求解过程成为一个最小化过程。利用A1给出的一类丢番图方程，说明了所提方法的有效性。x1 p1+a2。x2 p2+......+安。xn pn=N其中ai和N是整数。实验结果表明，所提出的方法在求解具有足够大幂次和大量变量的丢番图方程时是成功的。
---
英文标题：
《Steepest Ascent Hill Climbing For A Mathematical Problem》
---
作者：
Siby Abraham, Imre Kiss, Sugata Sanyal, Mukund Sanglikar
---
最新提交年份：
2010
---
分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
--
---
英文摘要：
The paper proposes artificial intelligence technique called hill climbing to find numerical solutions of Diophantine Equations. Such equations are important as they have many applications in fields like public key cryptography, integer factorization, algebraic curves, projective curves and data dependency in super computers. Importantly, it has been proved that there is no general method to find solutions of such equations. This paper is an attempt to find numerical solutions of Diophantine equations using steepest ascent version of Hill Climbing. The method, which uses tree representation to depict possible solutions of Diophantine equations, adopts a novel methodology to generate successors. The heuristic function used help to make the process of finding solution as a minimization process. The work illustrates the effectiveness of the proposed methodology using a class of Diophantine equations given by a1. x1 p1 + a2. x2 p2 + ...... + an . xn pn = N where ai and N are integers. The experimental results validate that the procedure proposed is successful in finding solutions of Diophantine Equations with sufficiently large powers and large number of variables.
---
PDF链接：
https://arxiv.org/pdf/1010.0298
京公网安备 11010802022788号
