{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T09:39:05Z","timestamp":1743068345305,"version":"3.40.3"},"publisher-location":"Cham","reference-count":17,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031198489"},{"type":"electronic","value":"9783031198496"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-19849-6_30","type":"book-chapter","created":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T15:03:32Z","timestamp":1666191812000},"page":"535-555","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Exploring a\u00a0Parallel SCC Algorithm"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4305-0625","authenticated-orcid":false,"given":"Jaco","family":"van de Pol","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,17]]},"reference":[{"issue":"1","key":"30_CR1","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1093\/logcom\/exp003","volume":"21","author":"J Barnat","year":"2011","unstructured":"Barnat, J., Chaloupka, J., van de Pol, J.: Distributed algorithms for SCC decomposition. J. Log. Comput. 21(1), 23\u201344 (2011). https:\/\/doi.org\/10.1093\/logcom\/exp003","journal-title":"J. Log. Comput."},{"key":"30_CR2","doi-asserted-by":"publisher","unstructured":"Bloemen, V.: Strong connectivity and shortest paths for checking models. Ph.D. thesis, University of Twente, July 2019. https:\/\/doi.org\/10.3990\/1.9789036547864","DOI":"10.3990\/1.9789036547864"},{"key":"30_CR3","doi-asserted-by":"publisher","unstructured":"Bloemen, V., Laarman, A., van de Pol, J.: Multi-core on-the-fly SCC decompositiona. In: PPOPP, pp. 8:1\u20138:12. ACM (2016). https:\/\/doi.org\/10.1145\/2851141.2851161","DOI":"10.1145\/2851141.2851161"},{"key":"30_CR4","doi-asserted-by":"publisher","unstructured":"Chen, R., Cohen, C., L\u00e9vy, J., Merz, S., Th\u00e9ry, L.: Formal proofs of Tarjan\u2019s strongly connected components algorithm in Why3, Coq and Isabelle. In: ITP, LIPIcs, vol. 141, pp. 13:1\u201313:19. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2019). https:\/\/doi.org\/10.4230\/LIPIcs.ITP.201a9.13","DOI":"10.4230\/LIPIcs.ITP.201a9.13"},{"key":"30_CR5","doi-asserted-by":"publisher","unstructured":"Dijkstra, E.W.: Finding the maximum strong components in a directed graph. In: Selected Writings on Computing: A Personal Perspective. Texts and Monographs in Computer Science, Springer, New York (1982). https:\/\/doi.org\/10.1007\/978-1-4612-5695-3","DOI":"10.1007\/978-1-4612-5695-3"},{"key":"30_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/978-3-642-39799-8_31","volume-title":"Computer Aided Verification","author":"J Esparza","year":"2013","unstructured":"Esparza, J., Lammich, P., Neumann, R., Nipkow, T., Schimpf, A., Smaus, J.-G.: A Fully verified executable LTL model checker. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 463\u2013478. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39799-8_31"},{"key":"30_CR7","doi-asserted-by":"publisher","unstructured":"Kuppe, M.A., Lamport, L., Ricketts, D.: The TLA+ toolbox. In: F-IDE@FM. EPTCS, vol. 310, pp. 50\u201362 (2019). https:\/\/doi.org\/10.4204\/EPTCS.310.6","DOI":"10.4204\/EPTCS.310.6"},{"key":"30_CR8","doi-asserted-by":"publisher","unstructured":"Lammich, P.: Verified efficient implementation of Gabow\u2019s strongly connected component algorithm. In: Klein, G., Gamboa, R. (eds.) Interactive Theorem Proving. ITP 2014, LNCS, vol. 8558. pp. 325\u2013340. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-08970-6_21","DOI":"10.1007\/978-3-319-08970-6_21"},{"issue":"2","key":"30_CR9","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10009-015-0382-1","volume":"18","author":"G Lowe","year":"2016","unstructured":"Lowe, G.: Concurrent depth-first search algorithms based on Tarjan\u2019s algorithm. Int. J. Softw. Tools Technol. Transf. 18(2), 129\u2013147 (2016). https:\/\/doi.org\/10.1007\/s10009-015-0382-1","journal-title":"Int. J. Softw. Tools Technol. Transf."},{"issue":"8","key":"30_CR10","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1016\/j.jpdc.2005.03.007","volume":"65","author":"W McLendon-III","year":"2005","unstructured":"McLendon-III, W., Hendrickson, B., Plimpton, S.J., Rauchwerger, L.: Finding strongly connected components in distributed graphs. J. Parallel Distrib. Comput. 65(8), 901\u2013910 (2005). https:\/\/doi.org\/10.1016\/j.jpdc.2005.03.007","journal-title":"J. Parallel Distrib. Comput."},{"key":"30_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-030-45190-5_14","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"W Oortwijn","year":"2020","unstructured":"Oortwijn, W., Huisman, M., Joosten, S.J.C., van de Pol, J.: Automated verification of parallel nested DFS. In: TACAS 2020. LNCS, vol. 12078, pp. 247\u2013265. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45190-5_14"},{"key":"30_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/978-3-319-19458-5_12","volume-title":"Formal Methods for Industrial Critical Systems","author":"JC Pol","year":"2015","unstructured":"Pol, J.C.: Automated verification of nested DFS. In: N\u00fa\u00f1ez, M., G\u00fcdemann, M. (eds.) FMICS 2015. LNCS, vol. 9128, pp. 181\u2013197. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-19458-5_12"},{"issue":"6","key":"30_CR13","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1007\/s10009-016-0422-5","volume":"19","author":"E Renault","year":"2017","unstructured":"Renault, E., Duret-Lutz, A., Kordon, F., Poitrenaud, D.: Variations on parallel explicit emptiness checks for generalized B\u00fcchi automata. Int. J. Softw. Tools Technol. Transf. 19(6), 653\u2013673 (2017). https:\/\/doi.org\/10.1007\/s10009-016-0422-5","journal-title":"Int. J. Softw. Tools Technol. Transf."},{"issue":"2","key":"30_CR14","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/0201010","volume":"1","author":"RE Tarjan","year":"1972","unstructured":"Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146\u2013160 (1972). https:\/\/doi.org\/10.1137\/0201010","journal-title":"SIAM J. Comput."},{"issue":"2","key":"30_CR15","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1145\/62.2160","volume":"31","author":"RE Tarjan","year":"1984","unstructured":"Tarjan, R.E., van Leeuwen, J.: Worst-case analysis of set union algorithms. J. ACM 31(2), 245\u2013281 (1984). https:\/\/doi.org\/10.1145\/62.2160","journal-title":"J. ACM"},{"key":"30_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/978-3-319-89960-2_4","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"S Wimmer","year":"2018","unstructured":"Wimmer, S., Lammich, P.: Verified model checking of timed automata. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10805, pp. 61\u201378. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-89960-2_4"},{"key":"30_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1007\/3-540-48153-2_6","volume-title":"Correct Hardware Design and Verification Methods","author":"Y Yu","year":"1999","unstructured":"Yu, Y., Manolios, P., Lamport, L.: Model checking TLA+ specifications. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 54\u201366. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48153-2_6"}],"container-title":["Lecture Notes in Computer Science","Leveraging Applications of Formal Methods, Verification and Validation. Verification Principles"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-19849-6_30","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T00:10:46Z","timestamp":1666224646000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-19849-6_30"}},"subtitle":["Using $$\\text {TLA}^{+}$$and the TLC Model Checker"],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031198489","9783031198496"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-19849-6_30","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"17 October 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ISoLA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Leveraging Applications of Formal Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rhodes","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Greece","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 October 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 October 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"isola2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.isola-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}