{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T11:00:49Z","timestamp":1768906849223,"version":"3.49.0"},"publisher-location":"Cham","reference-count":41,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030720155","type":"print"},{"value":"9783030720162","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,20]],"date-time":"2021-03-20T00:00:00Z","timestamp":1616198400000},"content-version":"vor","delay-in-days":78,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a reachability specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the performance of the synthesis and adaptively switches between inductive and deductive reasoning. Our experiments demonstrate that the novel CE construction provides a significantly faster and more effective pruning strategy leading to an accelerated synthesis process on a wide range of benchmarks. For challenging problems, such as the synthesis of decentralized partially-observable controllers, we reduce the run-time from a day to\u00a0minutes.<\/jats:p>","DOI":"10.1007\/978-3-030-72016-2_11","type":"book-chapter","created":{"date-parts":[[2021,3,19]],"date-time":"2021-03-19T22:03:37Z","timestamp":1616191417000},"page":"191-209","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Inductive Synthesis for Probabilistic Programs Reaches New Horizons"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1286-934X","authenticated-orcid":false,"given":"Roman","family":"Andriushchenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0300-9727","authenticated-orcid":false,"given":"Milan","family":"\u010ce\u0161ka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0978-8466","authenticated-orcid":false,"given":"Sebastian","family":"Junges","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6143-1926","authenticated-orcid":false,"given":"Joost-Pieter","family":"Katoen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,20]]},"reference":[{"key":"11_CR1","doi-asserted-by":"crossref","unstructured":"\u00c1brah\u00e1m, E., Becker, B., Dehnert, C., Jansen, N., Katoen, J.P., Wimmer, R.: Counterexample generation for discrete-time Markov models: An introductory survey. In: SFM. LNCS, vol.\u00a08483, pp. 65\u2013121. Springer (2014)","DOI":"10.1007\/978-3-319-07317-0_3"},{"key":"11_CR2","unstructured":"Alur, R., Bod\u00edk, R., Dallal, E., Fisman, D., Garg, P., Juniwal, G., Kress-Gazit, H., Madhusudan, P., Martin, M.M.K., Raghothaman, M., Saha, S., Seshia, S.A., Singh, R., Solar-Lezama, A., Torlak, E., Udupa, A.: Syntax-guided synthesis. In: Dependable Software Systems Engineering, NATO Science for Peace and Security Series, vol.\u00a040, pp. 1\u201325. IOS Press (2015)"},{"key":"11_CR3","doi-asserted-by":"crossref","unstructured":"Baier, C., de\u00a0Alfaro, L., Forejt, V., Kwiatkowska, M.: Model checking probabilistic systems. In: Handbook of Model Checking, pp. 963\u2013999. Springer (2018)","DOI":"10.1007\/978-3-319-10575-8_28"},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"Baier, C., Hensel, C., Hutschenreiter, L., Junges, S., Katoen, J., Klein, J.: Parametric markov chains: PCTL complexity and fraction-free gaussian elimination. Inf. Comput. 272, 104504 (2020)","DOI":"10.1016\/j.ic.2019.104504"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Bartocci, E., Grosu, R., Katsaros, P., Ramakrishnan, C.R., Smolka, S.A.: Model repair for probabilistic systems. In: TACAS\u201911. LNCS, vol.\u00a06605, pp. 326\u2013340 (2011)","DOI":"10.1007\/978-3-642-19835-9_30"},{"key":"11_CR6","doi-asserted-by":"crossref","unstructured":"Bornholt, J., Torlak, E., Grossman, D., Ceze, L.: Optimizing synthesis with metasketches. In: POPL\u201916. p. 775\u2013788. Association for Computing Machinery (2016)","DOI":"10.1145\/2914770.2837666"},{"key":"11_CR7","doi-asserted-by":"crossref","unstructured":"Calinescu, R., \u010ce\u0161ka, M., Gerasimou, S., Kwiatkowska, M., Paoletti, N.: Efficient synthesis of robust models for stochastic systems. J. of Systems and Softw. 143, 140\u2013158 (2018)","DOI":"10.1016\/j.jss.2018.05.013"},{"key":"11_CR8","doi-asserted-by":"crossref","unstructured":"\u010ce\u0161ka, M., Dannenberg, F., Paoletti, N., Kwiatkowska, M., Brim, L.: Precise parameter synthesis for stochastic biochemical systems. Acta Inf. 54(6), 589\u2013623 (2017)","DOI":"10.1007\/s00236-016-0265-2"},{"key":"11_CR9","doi-asserted-by":"crossref","unstructured":"\u010ce\u0161ka, M., Hensel, C., Junges, S., Katoen, J.P.: Counterexample-driven synthesis for probabilistic program sketches. In: FM. LNCS, vol. 11800, pp. 101\u2013120. Springer (2019)","DOI":"10.1007\/978-3-030-30942-8_8"},{"key":"11_CR10","doi-asserted-by":"crossref","unstructured":"\u010ce\u0161ka, M., Jansen, N., Junges, S., Katoen, J.P.: Shepherding hordes of Markov chains. In: TACAS (2). LNCS, vol. 11428, pp. 172\u2013190. Springer (2019)","DOI":"10.1007\/978-3-030-17465-1_10"},{"key":"11_CR11","unstructured":"Chatzieleftheriou, G., Katsaros, P.: Abstract model repair for probabilistic systems. Inf. Comput. 259(1), 142\u2013160 (2018)"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"Chonev, V.: Reachability in augmented interval Markov chains. In: RP\u20192019. LNCS, vol. 11674, pp. 79\u201392. Springer (2019)","DOI":"10.1007\/978-3-030-30806-3_7"},{"key":"11_CR13","doi-asserted-by":"crossref","unstructured":"Chrszon, P., Dubslaff, C., Kl\u00fcppelholz, S., Baier, C.: ProFeat: feature-oriented engineering for family-based probabilistic model checking. Formal Asp. Comput. 30(1), 45\u201375 (2018)","DOI":"10.1007\/s00165-017-0432-4"},{"key":"11_CR14","unstructured":"Classen, A., Cordy, M., Heymans, P., Legay, A., Schobbens, P.Y.: Model checking software product lines with SNIP. Int. J. on Softw. Tools for Technol. Transf. 14, 589\u2013612 (2012)"},{"key":"11_CR15","doi-asserted-by":"crossref","unstructured":"Daws, C.: Symbolic and parametric model checking of discrete-time Markov chains. In: ICTAC. LNCS, vol.\u00a03407, pp. 280\u2013294. Springer (2004)","DOI":"10.1007\/978-3-540-31862-0_21"},{"key":"11_CR16","doi-asserted-by":"crossref","unstructured":"Dehnert, C., Jansen, N., Wimmer, R., \u00c1brah\u00e1m, E., Katoen, J.P.: Fast debugging of PRISM models. In: ATVA. LNCS, vol.\u00a08837, pp. 146\u2013162. Springer (2014)","DOI":"10.1007\/978-3-319-11936-6_11"},{"key":"11_CR17","doi-asserted-by":"crossref","unstructured":"Dehnert, C., Junges, S., Jansen, N., Corzilius, F., Volk, M., Bruintjes, H., Katoen, J.P., \u00c1brah\u00e1m, E.: PROPhESY: A PRObabilistic ParamEter SYNnthesis Tool. In: CAV\u201915. LNCS, vol.\u00a09206, pp. 214\u2013231. Springer (2015)","DOI":"10.1007\/978-3-319-21690-4_13"},{"key":"11_CR18","doi-asserted-by":"crossref","unstructured":"Dehnert, C., Junges, S., Katoen, J.P., Volk, M.: A Storm is coming: A modern probabilistic model checker. In: CAV. LNCS, vol. 10427, pp. 592\u2013600. Springer (2017)","DOI":"10.1007\/978-3-319-63390-9_31"},{"key":"11_CR19","doi-asserted-by":"crossref","unstructured":"Funke, F., Jantsch, S., Baier, C.: Farkas certificates and minimal witnesses for probabilistic reachability constraints. In: TACAS (1). LNCS, vol. 12078, pp. 324\u2013345. Springer (2020)","DOI":"10.1007\/978-3-030-45190-5_18"},{"key":"11_CR20","unstructured":"Gerasimou, S., Calinescu, R., Tamburrelli, G.: Synthesis of probabilistic models for quality-of-service software engineering. Autom. Softw. Eng. 25(4), 785\u2013831 (2018)"},{"key":"11_CR21","unstructured":"Ghezzi, C., Sharifloo, A.M.: Model-based verification of quantitative non-functional properties for software product lines. Inf. & Softw. Technol. 55(3), 508\u2013524 (2013)"},{"key":"11_CR22","unstructured":"Hahn, E.M., Hermanns, H., Zhang, L.: Probabilistic reachability for parametric Markov models. Int. J. on Softw. Tools for Technol. Transf. 13(1), 3\u201319 (2011)"},{"key":"11_CR23","doi-asserted-by":"crossref","unstructured":"Harman, M., Mansouri, S.A., Zhang, Y.: Search-based software engineering: Trends, techniques and applications. ACM Comp. Surveys 45(1), 11:1\u201311:61 (2012)","DOI":"10.1145\/2379776.2379787"},{"key":"11_CR24","unstructured":"Herman, T.: Probabilistic self-stabilization. Inf. Process. Lett. 35(2), 63\u201367 (1990)"},{"key":"11_CR25","doi-asserted-by":"crossref","unstructured":"Jha, S., Gulwani, S., Seshia, S.A., Tiwari, A.: Oracle-guided component-based program synthesis. In: ICSE. p. 215\u2013224. ACM (2010)","DOI":"10.1145\/1806799.1806833"},{"key":"11_CR26","doi-asserted-by":"crossref","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic verification of Herman\u2019s self-stabilisation algorithm. Formal Aspects of Computing 24(4), 661\u2013670 (2012)","DOI":"10.1007\/s00165-012-0227-6"},{"key":"11_CR27","doi-asserted-by":"crossref","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: CAV. LNCS, vol.\u00a06806, pp. 585\u2013591. Springer (2011)","DOI":"10.1007\/978-3-642-22110-1_47"},{"key":"11_CR28","unstructured":"Lanna, A., Castro, T., Alves, V., Rodrigues, G., Schobbens, P.Y., Apel, S.: Feature-family-based reliability analysis of software product lines. Inf. and Softw. Technol. 94, 59\u201381 (2018)"},{"key":"11_CR29","doi-asserted-by":"crossref","unstructured":"Lindemann, C.: Performance modelling with deterministic and stochastic Petri nets. SIGMETRICS Perform. Eval. Rev. 26(2), \u00a03 (1998)","DOI":"10.1145\/288197.581195"},{"key":"11_CR30","unstructured":"Madani, O., Hanks, S., Condon, A.: On the undecidability of probabilistic planning and infinite-horizon partially observable Markov decision problems. In: AAAI\/IAAI. pp. 541\u2013548. AAAI Press \/ The MIT Press (1999)"},{"key":"11_CR31","doi-asserted-by":"crossref","unstructured":"Martens, A., Koziolek, H., Becker, S., Reussner, R.: Automatically improve software architecture models for performance, reliability, and cost using evolutionary algorithms. In: WOSP\/SIPEW. pp. 105\u2013116. ACM (2010)","DOI":"10.1145\/1712605.1712624"},{"key":"11_CR32","doi-asserted-by":"crossref","unstructured":"Nori, A.V., Ozair, S., Rajamani, S.K., Vijaykeerthy, D.: Efficient synthesis of probabilistic programs. In: PLDI\u201914. pp. 208\u2013217. ACM (2015)","DOI":"10.1145\/2813885.2737982"},{"key":"11_CR33","doi-asserted-by":"crossref","unstructured":"Oliehoek, F.A., Amato, C.: A Concise Introduction to Decentralized POMDPs. Springer Briefs in Intelligent Systems, Springer (2016)","DOI":"10.1007\/978-3-319-28929-8"},{"key":"11_CR34","doi-asserted-by":"crossref","unstructured":"Pathak, S., \u00c1brah\u00e1m, E., Jansen, N., Tacchella, A., Katoen, J.P.: A greedy approach for the efficient repair of stochastic models. In: NFM\u201915. LNCS, vol.\u00a09058, pp. 295\u2013309. Springer (2015)","DOI":"10.1007\/978-3-319-17524-9_21"},{"key":"11_CR35","doi-asserted-by":"crossref","unstructured":"Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Statistics, Wiley (1994)","DOI":"10.1002\/9780470316887"},{"key":"11_CR36","doi-asserted-by":"crossref","unstructured":"Quatmann, T., Dehnert, C., Jansen, N., Junges, S., Katoen, J.P.: Parameter synthesis for Markov models: Faster than ever. In: ATVA\u201916. LNCS, vol.\u00a09938, pp. 50\u201367 (2016)","DOI":"10.1007\/978-3-319-46520-3_4"},{"key":"11_CR37","doi-asserted-by":"crossref","unstructured":"Quatmann, T., Jansen, N., Dehnert, C., Wimmer, R., \u00c1brah\u00e1m, E., Katoen, J.P., Becker, B.: Counterexamples for expected rewards. In: FM. pp. 435\u2013452. Springer (2015)","DOI":"10.1007\/978-3-319-19249-9_27"},{"key":"11_CR38","doi-asserted-by":"crossref","unstructured":"Saad, F.A., Cusumano-Towner, M.F., Schaechtle, U., Rinard, M.C., Mansinghka, V.K.: Bayesian synthesis of probabilistic programs for automatic data modeling. Proceedings of the ACM on Programming Languages 3(POPL), 1\u201332 (2019)","DOI":"10.1145\/3290350"},{"key":"11_CR39","doi-asserted-by":"crossref","unstructured":"Solar-Lezama, A., Rabbah, R., Bod\u00edk, R., Ebcio\u011flu, K.: Programming by sketching for bit-streaming programs. In: PLDI\u201905. pp. 281\u2013294. ACM (2005)","DOI":"10.1145\/1064978.1065045"},{"key":"11_CR40","doi-asserted-by":"crossref","unstructured":"Vandin, A., ter Beek, M.H., Legay, A., Lluch-Lafuente, A.: Qflan: A tool for the quantitative analysis of highly reconfigurable systems. In: FM. LNCS, vol. 10951, pp. 329\u2013337. Springer (2018)","DOI":"10.1007\/978-3-319-95582-7_19"},{"key":"11_CR41","doi-asserted-by":"crossref","unstructured":"Wimmer, R., Jansen, N., Vorpahl, A., \u00c1brah\u00e1m, E., Katoen, J.P., Becker, B.: High-level counterexamples for probabilistic automata. Logical Methods in Computer Science 11(1) (2015)","DOI":"10.2168\/LMCS-11(1:15)2015"}],"container-title":["Lecture Notes in Computer Science","Tools and Algorithms for the Construction and Analysis of Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-72016-2_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:07:52Z","timestamp":1616371672000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-72016-2_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030720155","9783030720162"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-72016-2_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"20 March 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TACAS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Tools and Algorithms for the Construction and Analysis of Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Luxembourg City","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Luxembourg","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 March 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 April 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tacas2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2021\/tacas","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"141","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"41","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"21","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"29% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"12","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference changed to an online format due to the COVID-19 pandemic","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}