Formal Derivation of the Combinatorics Problems with PAR Method
ABSTRACT
Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving combinatorics problems. Furthermore, we formally derive combinatorics problems by PAR method, which cannot only simplify the process of algorithmic program's designing, but also improve its automatization, standardization and correctness. We develop algorithms for two typical combinatorics problems, the number of string scheme and the number of error per-mutation scheme. Lastly, we obtain accurate C++ programs which are transformed by automatic transforming system of PAR platform.
Partition-and-Recur (PAR) method is a simple and useful formal method. It can be used to design and testify algo-rithmic programs. In this paper, we propose that PAR method is an effective formal method on solving combinatorics problems. Furthermore, we formally derive combinatorics problems by PAR method, which cannot only simplify the process of algorithmic program's designing, but also improve its automatization, standardization and correctness. We develop algorithms for two typical combinatorics problems, the number of string scheme and the number of error per-mutation scheme. Lastly, we obtain accurate C++ programs which are transformed by automatic transforming system of PAR platform.
Cite this paper
nullL. SUN and Y. SUN, "Formal Derivation of the Combinatorics Problems with PAR Method," Journal of Software Engineering and Applications, Vol. 2 No. 3, 2009, pp. 195-199. doi: 10.4236/jsea.2009.23026.
nullL. SUN and Y. SUN, "Formal Derivation of the Combinatorics Problems with PAR Method," Journal of Software Engineering and Applications, Vol. 2 No. 3, 2009, pp. 195-199. doi: 10.4236/jsea.2009.23026.
References
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[1] J. Y. Xue, “A unified approach for developing efficient algorithmic programs [J],” Journal of computer Science and Technology, Vol. 12, No. 4, pp. 103–118, 1997. [2] J. Y. Xue, “Formal derivation of graph algorithmic programs using Partition-and-Recur [J],” Journal of Computer Sciences and Technology, Vol. 13, No. 6, pp. 95– 102, 1998. [3] J. Y. Xue, “A practicable approach for formal development of algorithmic programs [C],” The Proceedings of The international Symposium on Future software Technology (ISFS'99), Published by Software Engineers Associations of Japan, pp. 212–217, 1999. [4] L. Y. Sun, “The applied research of PAR method on combinatorics problems [D],” Jiangxi Normal University, 2007. [5] J. Y. Xue, “Research on formal development of algorithmic program [J],” Journal of Yunnan University (natural sciences), Vol. 19, pp. 283–288, 1997. [6] Y. Q. Li, “Partition-and-recur method and its applications [J],” Computer Engineering and Applications, Vo1. 27, No. 11, pp. 77–79, 2000. [7] L. Y. Sun and J. Y. Xue, “Formal derivation of the minimum spanning tree algorithm with PAR Method [J],” Computer Engineering, Vo1. 32, No. 21, pp. 85–87, 2007.