自动推理技术在求解组合数学难题中的研究进展  

Automated Reasoning Techniques for Solving Combinatorial Mathematical Problems:A Survey

作　　者：黄沛 刘明昊 马菲菲[2,3] 张健 HUANG Pei;LIU Minghao;MA Feifei;ZHANG Jian(State Key Laboratory of Computer Science,Institute of Software,Chinese Academy of Sciences,Beijing 100190,China;Laboratory of Parallel Software and Computational Science,Institute of Software,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院软件研究所计算机科学国家重点实验室,北京100190 [2]中国科学院软件研究所并行软件与计算科学实验室,北京100190 [3]中国科学院大学,北京100049

出　　处：《计算机科学》2023年第7期167-175,共9页Computer Science

基　　金：国家自然科学基金(61972384,62132020)。

摘　　要：自动推理是一种以符号演算的方式来自动模拟人类逻辑推理能力的技术,其总体目标是利用计算机构建一个将不同形式的推理机械化的系统。虽然该领域的理论框架尚未实现对人类全部推理能力的模拟,但该领域的发展已经可以帮助研究人员解决一些数学和逻辑领域的开放性问题,并提供了计算科学中的重要应用。文中简要回顾了利用自动推理技术处理组合数学开放性难题时的代表性方法,重点梳理了该领域的国内外最新进展,分析了各种方法的优势与不足,介绍了近年来出现的增强自动推理结果可信性的技术方法,并探讨了未来的研究方向和面临的挑战。Automated reasoning is a symbolic algorithmic technique that aims to simulate the logical reasoning ability of human.The overall goal is to mechanize different forms of reasoning with a computer system.Although the theoretical framework of the field has not yet supported the simulation of the full range of human reasoning capabilities,developments in the field have reached a point where automated reasoning programs are being used by researchers to attack open problems in mathematics and logic and provide important applications in computing science.This paper briefly reviews common approaches of automatic reasoning in dealing with open problems in combinatorial mathematics and highlights the latest developments in this field in China and abroad.Then the strengths and weaknesses of various approaches are analyzed,and reasoning strategies that have emerged in recent years to enhance the trustworthiness of automated reasoning results are introduced.Finally,future research directions and challenges are discussed.

关 键 词：自动推理 组合数学 计算逻辑 人工智能 符号演算 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]