形式化开发若干组合数学问题的算法

Formal Development of Several Algorithms for Combinatorial Mathematics Problems

计算机科学的核心内容是使用算法处理离散数据,组合数学的重要性日渐凸显.使用形式化方法PAR开发了两个组合数学问题的算法,形式化推导过程为问题求解提供了思路,自然地引进了算法程序中用到的变量,清晰地展示了算法程序的设计过程,最终可得到简洁、易理解、可靠性高的算法程序.对形式化方法开发组合算法做了积极的探索,有利于促进组合算法设计自动化的研究及形式化开发方法的推广应用.

The core of computer science is handling discrete data employing algorithms, so combinatorics is becoming more and more important. The paper develops two algorithmic programs of combinatorics problems using the formal method PAR. Formal derivation provides clues for solving the problems and can find other intimate definitions that will be used in algorithms, through which achieves concise, readable, high performance and reliability algorithmic programs finally. The paper explores the application of formal methods to combinatorial algorithms, and contributes to the research of automatic algorithm design for combinatorial algorithms and the extensive employment of formal development methods.