{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:22:11Z","timestamp":1742916131607,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540402534"},{"type":"electronic","value":"9783540448808"}],"license":[{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-44880-2_16","type":"book-chapter","created":{"date-parts":[[2007,7,3]],"date-time":"2007-07-03T16:12:53Z","timestamp":1183479173000},"page":"240-259","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Probabilistic Invariants for Probabilistic Machines"],"prefix":"10.1007","author":[{"given":"Thai Son","family":"Hoang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhendong","family":"Jin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ken","family":"Robinson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Annabelle","family":"McIver","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carroll","family":"Morgan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2003,5,27]]},"reference":[{"key":"16_CR1","unstructured":"Probabilistic symbolic model checker. http:\/\/www.cs.bham.ac.uk\/~dxp\/prism\/publications.html."},{"key":"16_CR2","unstructured":"Specification and development of probabilistic systems. http:\/\/web.comlab.ox.ac.uk\/oucl\/research\/areas\/probs\/."},{"key":"16_CR3","unstructured":"Proceeding of the 3rd International Conference of B and Z Users. Springer, 2003."},{"key":"16_CR4","doi-asserted-by":"crossref","unstructured":"J-R. Abrial. The B-Book. Cambridge University Press, 1996.","DOI":"10.1017\/CBO9780511624162"},{"key":"16_CR5","unstructured":"B-Core(UK) Ltd. B Toolkit. http:\/\/www.b-core.com."},{"key":"16_CR6","unstructured":"John E. Freund. John E. Freund\u2019s Mathematical Statistics. Prentice Hall International, Inc., 6 edition, 1999."},{"key":"16_CR7","doi-asserted-by":"crossref","unstructured":"D. Gries and J. Prins. A new notion of encapsulation. In Symposium on Language Issues in Programming Environments. SIGPLAN, June 1985.","DOI":"10.1145\/800225.806834"},{"key":"16_CR8","unstructured":"A. K. McIver. Quantitative program logic and counting rounds in probabilistic distributed algorithms. In Proc. 5th Intl. Workshop ARTS\u2019 99, volume 1601, 1999."},{"key":"16_CR9","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s002360000046","volume":"37","author":"A. K. McIver","year":"2001","unstructured":"A. K. McIver and C. C. Morgan. Demonic, angelic and unbounded probabilistic choices in sequential programs. Acta Informatica, 37:329\u2013354, 2001.","journal-title":"Acta Informatica"},{"issue":"3","key":"16_CR10","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1145\/229542.229547","volume":"18","author":"C. C. Morgan","year":"1996","unstructured":"C. C. Morgan, A. K. McIver, and K. Seidel. Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems, 18(3):325\u2013353, May 1996.","journal-title":"ACM Transactions on Programming Languages and Systems"},{"key":"16_CR11","unstructured":"A. K. McIver, C. C. Morgan, and Thai Son Hoang. Probabilistic termination in B. In Proceeding of the 3rd International Conference of B and Z Users [3]."},{"key":"16_CR12","unstructured":"C. C. Morgan. Programming from Specifications. Prentice-Hall, second edition, 1994. At http:\/\/web.comlab.ox.ac.uk\/oucl\/publications\/books\/PfS."},{"key":"16_CR13","series-title":"Lect Notes Comput Sci","volume-title":"Proceedings B\u201998: the 2nd International B Conference","author":"C. C. Morgan","year":"1998","unstructured":"C. C. Morgan. The generalised substitution language extended to probabilistic programs. In Proceedings B\u201998: the 2nd International B Conference, volume 1393 of LNCS, Montpelier, April 1998. Also available at [2, B98]."},{"key":"16_CR14","series-title":"Lect Notes Comput Sci","volume-title":"Proceedings of the 5th AMAST workshop on real time and probabilistic systems Bamberg, Germany, ARTS\u2019 1999","author":"Stoelinga","year":"1996","unstructured":"Stoelinga and Vaandrager. Root contention in IEEE 1394. In Proceedings of the 5th AMAST workshop on real time and probabilistic systems Bamberg, Germany, ARTS\u2019 1999, volume 1061 of LNCS."}],"container-title":["Lecture Notes in Computer Science","ZB 2003: Formal Specification and Development in Z and B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-44880-2_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T21:00:17Z","timestamp":1683925217000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/3-540-44880-2_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540402534","9783540448808"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/3-540-44880-2_16","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2003]]},"assertion":[{"value":"27 May 2003","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}