Reachability determination in acyclic Petri nets by cell enumeration approach

Authors:
Duan Li;Xiaoling Sun;Jianjun Gao;Shenshen Gu;Xiaojin Zheng
Affiliations:
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Management Science, School of Management, Fudan University, Shanghai, China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, China;School of Economics and Management, Tongji University, Shanghai 200092, China
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

Reachability is one of the most important behavioral properties of Petri nets. We propose in this paper a novel approach for solving the fundamental equation in the reachability analysis of acyclic Petri nets, which has been known to be NP-complete. More specifically, by adopting a revised version of the cell enumeration method for an arrangement of hyperplanes in discrete geometry, we develop an efficient solution scheme to identify firing count vector solution(s) to the fundamental equation on a bounded integer set, with a complexity bound of O((nu)^n^-^m), where n is the number of transitions, m is the number of places and u is the upper bound of the number of firings for all individual transitions.