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Journal of Applied Mathematics
Volume 2014, Article ID 352152, 20 pages
Research Article

Unified Mathematical Framework for Slicing and Symmetry Reduction over Event Structures

1G&S Labs, School of Software, Dalian University of Technology, Dalian 116620, China
2School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
3School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China

Received 28 January 2014; Accepted 27 April 2014; Published 12 June 2014

Academic Editor: Xiaoyu Song

Copyright © 2014 Xinyan Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonclassical slicing and symmetry reduction can act as efficient structural abstract methods for pruning state space when dealing with verification problems. In this paper, we mainly address theoretical and algorithmic aspects for nonclassical slicing and symmetry reduction over prime event structures. We propose sliced and symmetric quotient reduction models of event structures and present their corresponding algorithms. To construct the underlying foundation of the proposed methodologies, we introduce strong and weak conflict concepts and a pair of mutually inverse operators and extend permutation group based symmetry notion of event structures. We have established a unified mathematical framework for slicing and symmetry reduction, and further investigated the translation, isomorphism, and equivalence relationship and other related basic facts from a theoretical point of view. The framework may provide useful guidance and theoretical exploration for overcoming verification challenges. This paper also demonstrates their practical applications by two cases.