{"title":"A Disconnected 1-Safe Petri Net Whose Reachability Tree Is Homomorphic to a Complete Boolean Lattice","authors":"Sangita Kansal, G. Singh, M. Acharya","doi":"10.1109/PACC.2011.5979037","DOIUrl":null,"url":null,"abstract":"Petri nets generating all the 2^n binary n-vectors as their marking vectors are not only of theoretical interest but also are of practical importance. In this note, we demonstrate the existence of a disconnected 1-safe Petri net whose reachability tree is homomorphic to the n-dimensional complete lattice L_n. This makes the problem of characterizing the 1-safe Petri nets that generate all the binary n-vectors as marking vectors exactly once appear more intricate.","PeriodicalId":403612,"journal":{"name":"2011 International Conference on Process Automation, Control and Computing","volume":"95 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 International Conference on Process Automation, Control and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PACC.2011.5979037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
Petri nets generating all the 2^n binary n-vectors as their marking vectors are not only of theoretical interest but also are of practical importance. In this note, we demonstrate the existence of a disconnected 1-safe Petri net whose reachability tree is homomorphic to the n-dimensional complete lattice L_n. This makes the problem of characterizing the 1-safe Petri nets that generate all the binary n-vectors as marking vectors exactly once appear more intricate.
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