{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:54Z","timestamp":1760060694336,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T00:00:00Z","timestamp":1758585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Software"],"abstract":"<jats:p>This paper introduces a variant of the classic Towers of Hanoi (TH) puzzle in which parallel moves\u2014simultaneous transfers of multiple discs\u2014are permitted. The problem is formalized with Generalized Nets (GN), an extension of Petri nets (PN) whose tokens and transitions encode the ordering and movement of the n discs among three rods under the usual constraints. The resulting GN model, implemented on the OnlineGN platform, provides a clear, precise, and systematic representation that highlights the role of parallelism and supports interactive experimentation. This framework enables the exploration of strategies that reduce the number of parallel steps (PS) and, more broadly, illustrates how GN-captured parallelism can shorten the sequential depth for selected problems with exponential-time solutions.<\/jats:p>","DOI":"10.3390\/software4040023","type":"journal-article","created":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T14:32:53Z","timestamp":1758637973000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Parallel Towers of Hanoi via Generalized Nets: Simulated with OnlineGN"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1412-7606","authenticated-orcid":false,"given":"Angel","family":"Dimitriev","sequence":"first","affiliation":[{"name":"Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria"},{"name":"Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5625-071X","authenticated-orcid":false,"given":"Krassimir","family":"Atanassov","sequence":"additional","affiliation":[{"name":"Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2697-9766","authenticated-orcid":false,"given":"Nora","family":"Angelova","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, Sofia University \u201cSt. Kliment Ohridski\u201d, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hinz, A.M., Klav\u017ear, S., Milutinovi\u0107, U., and Petr, C. (2013). The Tower of Hanoi\u2014Myths and Maths, Birkh\u00e4user.","DOI":"10.1007\/978-3-0348-0237-6"},{"key":"ref_2","first-page":"596","article-title":"Solution of the Tower of Hanoi Problem","volume":"52","author":"Frame","year":"1945","journal-title":"Am. Math. Mon."},{"key":"ref_3","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., and Stein, C. (2009). Introduction to Algorithms, MIT Press. 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