{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T01:18:08Z","timestamp":1743124688940,"version":"3.40.3"},"publisher-location":"Cham","reference-count":11,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031635007"},{"type":"electronic","value":"9783031635014"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T00:00:00Z","timestamp":1719878400000},"content-version":"vor","delay-in-days":183,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The predicate definitions in Separation Logic (SL) play an important role: they capture a large spectrum of unbounded heap shapes due to their inductiveness. This expressiveness power comes with a limitation: the entailment problem is undecidable if predicates have general inductive definitions (ID). Iosif et al.\u00a0[8] proposed syntactic and semantic conditions, called PCE, on the ID of predicates to ensure the decidability of the entailment problem. We provide a (possibly nonterminating) algorithm to transform arbitrary ID into equivalent PCE definitions when possible. We show that the existence of an equivalent PCE definition for a given ID is undecidable, but we identify necessary conditions that are decidable. The algorithm has been implemented, and experimental results are reported on a benchmark, including significant examples from .<\/jats:p>","DOI":"10.1007\/978-3-031-63501-4_9","type":"book-chapter","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T09:02:00Z","timestamp":1719824520000},"page":"157-175","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["What Is Decidable in\u00a0Separation Logic Beyond Progress, Connectivity and\u00a0Establishment?"],"prefix":"10.1007","author":[{"given":"Tanguy","family":"Bozec","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8943-7000","authenticated-orcid":false,"given":"Nicolas","family":"Peltier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6504-8336","authenticated-orcid":false,"given":"Quentin","family":"Petitjean","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1925-089X","authenticated-orcid":false,"given":"Mihaela","family":"Sighireanu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,2]]},"reference":[{"key":"9_CR1","unstructured":"SL-COMP website. https:\/\/sl-comp.github.io\/"},{"key":"9_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1007\/978-3-642-35182-2_25","volume-title":"Programming Languages and Systems","author":"J Brotherston","year":"2012","unstructured":"Brotherston, J., Gorogiannis, N., Petersen, R.L.: A generic cyclic theorem prover. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 350\u2013367. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-35182-2_25"},{"key":"9_CR3","doi-asserted-by":"publisher","unstructured":"Echenim, M., Iosif, R., Peltier, N.: Entailment checking in separation logic with inductive definitions is 2-EXPTIME hard. In: Albert, E., Kovacs, L. (eds.) LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol. 73. EPiC Series in Computing, pp. 191\u2013211. EasyChair, May 2020. ISSN: 2398-7340. https:\/\/easychair.org\/publications\/paper\/DdNg, https:\/\/doi.org\/10.29007\/f5wh","DOI":"10.29007\/f5wh"},{"key":"9_CR4","doi-asserted-by":"publisher","unstructured":"Echenim, M., Iosif, R., Peltier., N.: Decidable entailments in separation logic with inductive definitions: beyond establishment. In: Baier, C., Goubault-Larrecq, J. (eds.) 29th EACSL Annual Conference on Computer Science Logic (CSL 2021), vol. 183. Leibniz International Proceedings in Informatics (LIPIcs), pp. 20:1\u201320:18, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik. https:\/\/drops.dagstuhl.de\/entities\/document\/10.4230\/ LIPIcs.CSL.2021.20, https:\/\/doi.org\/10.4230\/LIPIcs.CSL.2021.20","DOI":"10.4230\/LIPIcs.CSL.2021.20"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-3-030-79876-5_11","volume-title":"Automated Deduction \u2013 CADE 28","author":"M Echenim","year":"2021","unstructured":"Echenim, M., Iosif, R., Peltier, N.: Unifying decidable entailments in separation logic with inductive definitions. In: Platzer, A., Sutcliffe, G. (eds.) CADE 2021. LNCS (LNAI), vol. 12699, pp. 183\u2013199. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-79876-5_11"},{"key":"9_CR6","doi-asserted-by":"publisher","unstructured":"Echenim, M., Iosif, R., Peltier, N.: Entailment is Undecidable for Symbolic Heap Separation Logic Formul\u00e6 with Non-Established Inductive Rules. Inf. Process. Lett. 173:106169, January 2022. https:\/\/www.sciencedirect.com\/science\/article\/pii\/ S0020019021000843, https:\/\/doi.org\/10.1016\/j.ipl.2021.106169","DOI":"10.1016\/j.ipl.2021.106169"},{"key":"9_CR7","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1007\/978-3-319-40229-1_36","volume-title":"Automated Reasoning","author":"X Gu","year":"2016","unstructured":"Gu, X., Chen, T., Wu, Z.: A complete decision procedure for linearly compositional separation logic with data constraints. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 532\u2013549. 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