{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T13:57:20Z","timestamp":1761487040718},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2003,8]]},"abstract":"<jats:p> A Petri net (N, M<jats:sub>0<\/jats:sub>) is monotonically live (m-live) if it remains live when the values of its initial marking M<jats:sub>0<\/jats:sub> are increased. N is structurally m-live if there exists an initial marking M<jats:sub>0<\/jats:sub> such that (N, M<jats:sub>0<\/jats:sub>) is m-live. Three new siphon-based characterizations for these properties are obtained: (1) For a weighted net N, the ST-property (i.e., every siphon contains a trap) is a necessary but not sufficient condition for N to be structurally m-live. (2) For a weighted net N, a necessary but not sufficient condition for (N, M<jats:sub>0<\/jats:sub>) to be m-live is that every siphon of N contains an M<jats:sub>0<\/jats:sub>-controlled trap (i.e., for every reachable marking M, the trap contains a place whose token value is not smaller than the least weight of its outgoing arcs). (3) A homogeneous asymmetric choice net (N, M<jats:sub>0<\/jats:sub>) is m-live if and only if every minimal siphon of N contains an M<jats:sub>0<\/jats:sub>-controlled trap. Characterization (3) is a generalization of Commoner's Theorem from ordinary liveness for ordinary free choice nets to m-liveness for homogeneous asymmetric choice nets. <\/jats:p>","DOI":"10.1142\/s0129054103001935","type":"journal-article","created":{"date-parts":[[2003,9,19]],"date-time":"2003-09-19T10:19:32Z","timestamp":1063966772000},"page":"641-658","source":"Crossref","is-referenced-by-count":4,"title":["Characterizing Liveness Monotonicity for Weighted Petri Nets  in Terms of Siphon-Based Properties"],"prefix":"10.1142","volume":"14","author":[{"given":"Li","family":"Jiao","sequence":"first","affiliation":[{"name":"Department of Computer Science, City University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"To-Yat","family":"Cheung","sequence":"additional","affiliation":[{"name":"Department of Computer Science, City University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61363-3_4"},{"key":"rf3","first-page":"793","volume":"13","author":"Chu F.","journal-title":"IEEE Transactions on Robotics and Automation"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-55676-1_8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526558"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48068-4_13"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/5.24143"},{"key":"rf10","unstructured":"A.\u00a0Ohta and T.\u00a0Hisamura, Bulleten of Science and Engineering Research Laboratory (Waseda University, 1992)\u00a0pp. 91\u201398."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00124-7"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3126-5"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/3376"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054103001935","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:38:02Z","timestamp":1565138282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054103001935"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,8]]}},"alternative-id":["10.1142\/S0129054103001935"],"URL":"https:\/\/doi.org\/10.1142\/s0129054103001935","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,8]]}}}