Unified Mathematical Framework for Slicing and Symmetry Reduction over Event Structures. (12th June 2014)

• Record Type: Journal Article
• Authors: Gao, Xinyan; Ding, Yingcai; Liu, Wenbo; Zheng, Kaidi; Huang, Siyu; Zhou, Ning; Li, Dakui
• Other Names: Song Xiaoyu Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-06-12
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/352152
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.