{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T20:21:50Z","timestamp":1751660510833},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642388552"},{"type":"electronic","value":"9783642388569"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38856-9_5","type":"book-chapter","created":{"date-parts":[[2013,6,15]],"date-time":"2013-06-15T00:05:28Z","timestamp":1371254728000},"page":"43-62","source":"Crossref","is-referenced-by-count":33,"title":["The Abstract Domain of Segmented Ranking Functions"],"prefix":"10.1007","author":[{"given":"Caterina","family":"Urban","sequence":"first","affiliation":[]}],"member":"297","reference":[{"issue":"2","key":"5_CR1","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10817-010-9174-1","volume":"46","author":"E. Albert","year":"2011","unstructured":"Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. J. Autom. Reasoning\u00a046(2), 161\u2013203 (2011)","journal-title":"J. Autom. Reasoning"},{"key":"5_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/978-3-642-15769-1_8","volume-title":"Static Analysis","author":"C. Alias","year":"2010","unstructured":"Alias, C., Darte, A., Feautrier, P., Gonnord, L.: Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol.\u00a06337, pp. 117\u2013133. Springer, Heidelberg (2010)"},{"key":"5_CR3","doi-asserted-by":"crossref","unstructured":"Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O\u2019Hearn, P.W.: Variance Analyses from Invariance Analyses. In: POPL, pp. 211\u2013224 (2007)","DOI":"10.1145\/1190215.1190249"},{"key":"5_CR4","doi-asserted-by":"crossref","unstructured":"Bourdoncle, F.: Efficient Chaotic Iteration Strategies with Widenings. In: FMPA, pp. 128\u2013141 (1993)","DOI":"10.1007\/BFb0039704"},{"key":"5_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1007\/11523468_109","volume-title":"Automata, Languages and Programming","author":"A.R. Bradley","year":"2005","unstructured":"Bradley, A.R., Manna, Z., Sipma, H.B.: The Polyranking Principle. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol.\u00a03580, pp. 1349\u20131361. Springer, Heidelberg (2005)"},{"key":"5_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/978-3-540-70545-1_32","volume-title":"Computer Aided Verification","author":"B. Cook","year":"2008","unstructured":"Cook, B., Gulwani, S., Lev-Ami, T., Rybalchenko, A., Sagiv, M.: Proving Conditional Termination. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol.\u00a05123, pp. 328\u2013340. Springer, Heidelberg (2008)"},{"key":"5_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/11817963_37","volume-title":"Computer Aided Verification","author":"B. Cook","year":"2006","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: TERMINATOR: Beyond Safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol.\u00a04144, pp. 415\u2013418. Springer, Heidelberg (2006)"},{"issue":"5","key":"5_CR8","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1145\/1941487.1941509","volume":"54","author":"B. Cook","year":"2011","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: Proving Program Termination. Commun. ACM\u00a054(5), 88\u201398 (2011)","journal-title":"Commun. ACM"},{"key":"5_CR9","unstructured":"Cousot, P., Cousot, R.: Static Determination of Dynamic Properties of Programs. In: Proceedings of the Second International Symposium on Programming, pp. 106\u2013130 (1976)"},{"key":"5_CR10","doi-asserted-by":"crossref","unstructured":"Cousot, P., Cousot, R.: Abstract Interpretation: a Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In: POPL, pp. 238\u2013252 (1977)","DOI":"10.1145\/512950.512973"},{"issue":"2&3","key":"5_CR11","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/0743-1066(92)90030-7","volume":"13","author":"P. Cousot","year":"1992","unstructured":"Cousot, P., Cousot, R.: Abstract Interpretation and Application to Logic Programs. J. Log. Program.\u00a013(2&3), 103\u2013179 (1992)","journal-title":"J. Log. Program."},{"issue":"4","key":"5_CR12","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1093\/logcom\/2.4.511","volume":"2","author":"P. Cousot","year":"1992","unstructured":"Cousot, P., Cousot, R.: Abstract Interpretation Frameworks. J. Log. Comput.\u00a02(4), 511\u2013547 (1992)","journal-title":"J. Log. Comput."},{"key":"5_CR13","unstructured":"Cousot, P., Cousot, R.: Higher Order Abstract Interpretation (and Application to Comportment Analysis Generalizing Strictness, Termination, Projection, and PER Analysis. In: ICCL, pp. 95\u2013112 (1994)"},{"key":"5_CR14","doi-asserted-by":"crossref","unstructured":"Cousot, P., Cousot, R.: An Abstract Interpretation Framework for Termination. In: POPL, pp. 245\u2013258 (2012)","DOI":"10.1145\/2103621.2103687"},{"key":"5_CR15","doi-asserted-by":"crossref","unstructured":"Cousot, P., Cousot, R., Logozzo, F.: A Parametric Segmentation Functor for Fully Automatic and Scalable Array Content Analysis. In: POPL, pp. 105\u2013118 (2011)","DOI":"10.1145\/1925844.1926399"},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"Cousot, P., Halbwachs, N.: Automatic Discovery of Linear Restraints Among Variables of a Program. In: POPL, pp. 84\u201396 (1978)","DOI":"10.1145\/512760.512770"},{"key":"5_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/978-3-540-30579-8_3","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"J. Feret","year":"2005","unstructured":"Feret, J.: The Arithmetic-Geometric Progression Abstract Domain. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol.\u00a03385, pp. 42\u201358. Springer, Heidelberg (2005)"},{"key":"5_CR18","doi-asserted-by":"crossref","unstructured":"Floyd, R.W.: Assigning Meanings to Programs. In: Proceedings of Symposium on Applied Mathematics, vol.\u00a019, pp. 19\u201332 (1967)","DOI":"10.1090\/psapm\/019\/0235771"},{"issue":"1","key":"5_CR19","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1024480913162","volume":"23","author":"B. Jeannet","year":"2003","unstructured":"Jeannet, B.: Dynamic Partitioning in Linear Relation Analysis: Application to the Verification of Reactive Systems. Formal Methods in System Design\u00a023(1), 5\u201337 (2003)","journal-title":"Formal Methods in System Design"},{"key":"5_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/978-3-642-02658-4_52","volume-title":"Computer Aided Verification","author":"B. Jeannet","year":"2009","unstructured":"Jeannet, B., Min\u00e9, A.: Apron: A Library of Numerical Abstract Domains for Static Analysis. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol.\u00a05643, pp. 661\u2013667. Springer, Heidelberg (2009)"},{"issue":"1","key":"5_CR21","first-page":"31","volume":"19","author":"A. Min\u00e9","year":"2006","unstructured":"Min\u00e9, A.: The Octagon Abstract Domain. HOSC\u00a019(1), 31\u2013100 (2006)","journal-title":"HOSC"},{"key":"5_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/978-3-540-24622-0_20","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"A. Podelski","year":"2004","unstructured":"Podelski, A., Rybalchenko, A.: A Complete Method for the Synthesis of Linear Ranking Functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol.\u00a02937, pp. 239\u2013251. Springer, Heidelberg (2004)"},{"key":"5_CR23","doi-asserted-by":"crossref","unstructured":"Podelski, A., Rybalchenko, A.: Transition Invariants. In: LICS, pp. 32\u201341 (2004)","DOI":"10.1109\/LICS.2004.1319598"},{"key":"5_CR24","doi-asserted-by":"crossref","unstructured":"Rival, X., Mauborgne, L.: The Trace Partitioning Abstract Domain. ACM Transactions on Programming Languages and Systems\u00a029(5) (2007)","DOI":"10.1145\/1275497.1275501"},{"key":"5_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/978-3-642-19835-9_9","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"A. Tsitovich","year":"2011","unstructured":"Tsitovich, A., Sharygina, N., Wintersteiger, C.M., Kroening, D.: Loop Summarization and Termination Analysis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol.\u00a06605, pp. 81\u201395. Springer, Heidelberg (2011)"},{"key":"5_CR26","unstructured":"Turing, A.: Checking a Large Routine. In: Report of a Conference on High Speed Automatic Calculating Machines, pp. 67\u201369 (1948)"}],"container-title":["Lecture Notes in Computer Science","Static Analysis"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38856-9_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T00:59:58Z","timestamp":1557795598000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-38856-9_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642388552","9783642388569"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38856-9_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}