{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T14:27:52Z","timestamp":1745677672877,"version":"3.40.3"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031308284"},{"type":"electronic","value":"9783031308291"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T00:00:00Z","timestamp":1682035200000},"content-version":"vor","delay-in-days":110,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"abstract":"Abstract<\/jats:title>Given a textual representation of a finite-state concurrent program$$P$$<\/jats:tex-math>P<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, one can construct the corresponding Kripke structure$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. However, the size of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>can be exponentially larger than the textual size of$$P$$<\/jats:tex-math>P<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This state explosion can make model checking properties of$$P$$<\/jats:tex-math>P<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>via$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>expensive or even infeasible. The action of a symmetry group$$G$$<\/jats:tex-math>G<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>on$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>can be used to produce a smaller Kripke structure$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Various authors have exploited the direct correspondence between$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>to perform model checking. When the structure$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>does not satisfy a formula, one can look for a substructure that will satisfy the formula. We call thissubstructure-repair<\/jats:italic>: identifying a substructure$$\\mathcal {N}$$<\/jats:tex-math>N<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>that satisfies a given temporal logic formula.<\/jats:p>In this paper we extend previous work by showing that repairs of$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>lift to repairs of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In other words, we can repair a computer program$$P$$<\/jats:tex-math>P<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which exhibits a high degree of symmetry, by repairing the smaller Kripke structure$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and then symmetrizing the corresponding program. To do this we arrange the substructures of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>into substructure lattices that are ordered by substructure inclusion. We show that the substructures of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>preserved by$$G$$<\/jats:tex-math>G<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>form a (sub)lattice that maps to the substructure lattice of$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. When restricted to the lattice of substructures of$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>that are \u201cmaximal\u201d with the action of$$G$$<\/jats:tex-math>G<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>on$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the above map is a lattice isomorphism.<\/jats:p>These results enable us to repair$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and then to lift the repair to$$\\mathcal {M}$$<\/jats:tex-math>M<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In cases where a program has a high degree of symmetry, such as in many concurrent programs, we can repair the program by repairing the small Kripke structure$$\\overline{\\mathcal {M}}$$<\/jats:tex-math>M<\/mml:mi>\u00af<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/978-3-031-30829-1_25","type":"book-chapter","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T19:56:19Z","timestamp":1682020579000},"page":"520-540","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Model and Program Repair via Group Actions"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1989-0974","authenticated-orcid":false,"given":"Paul C.","family":"Attie","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0732-6666","authenticated-orcid":false,"given":"William L.","family":"Cocke","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,21]]},"reference":[{"key":"25_CR1","doi-asserted-by":"publisher","unstructured":"Aminof, B., Jacobs, S., Khalimov, A., Rubin, S.: Parameterized model checking of token-passing systems. In: McMillan, K.L., Rival, X. (eds.) Verification, Model Checking, and Abstract Interpretation - 15th International Conference, VMCAI 2014, San Diego, CA, USA, January 19-21, 2014, Proceedings. Lecture Notes in Computer Science, vol.\u00a08318, pp. 262\u2013281. Springer (2014). https:\/\/doi.org\/10.1007\/978-3-642-54013-4_15","DOI":"10.1007\/978-3-642-54013-4_15"},{"key":"25_CR2","doi-asserted-by":"publisher","unstructured":"Attie, P.C., Dak-Al-Bab, K., Sakr, M.: Model and program repair via SAT solving. ACM Trans. Embed. Comput. Syst. 17(2), 32:1\u201332:25 (2018). https:\/\/doi.org\/10.1145\/3147426","DOI":"10.1145\/3147426"},{"key":"25_CR3","doi-asserted-by":"publisher","unstructured":"Attie, P.C., Emerson, E.A.: Synthesis of concurrent systems with many similar processes. ACM Trans. Program. Lang. Syst. 20(1), 51\u2013115 (jan 1998). https:\/\/doi.org\/10.1145\/271510.271519","DOI":"10.1145\/271510.271519"},{"key":"25_CR4","doi-asserted-by":"publisher","unstructured":"Attie, P.C., Emerson, E.A.: Synthesis of concurrent programs for an atomic read\/write model of computation. ACM Trans. Program. Lang. Syst. 23(2), 187\u2013242 (mar 2001). https:\/\/doi.org\/10.1145\/383043.383044","DOI":"10.1145\/383043.383044"},{"key":"25_CR5","doi-asserted-by":"crossref","unstructured":"Buccafurri, F., Eiter, T., Gottlob, G., Leone, N.: Enhancing model checking in verification by AI techniques. Artif. Intell. 112, 57\u2013104 (1999)","DOI":"10.1016\/S0004-3702(99)00039-9"},{"key":"25_CR6","doi-asserted-by":"crossref","unstructured":"Chatzieleftheriou, G., Bonakdarpour, B., Smolka, S., Katsaros, P.: Abstract model repair. In: Goodloe, A., Person, S. (eds.) NASA Formal Methods, Lecture Notes in Computer Science, vol.\u00a07226, pp. 341\u2013355. Springer Berlin Heidelberg, Norfolk, VA, USA (2012)","DOI":"10.1007\/978-3-642-28891-3_32"},{"key":"25_CR7","doi-asserted-by":"crossref","unstructured":"Clarke, E.M., Emerson, E.A., Jha, S., Sistla, A.P.: Symmetry reductions in model checking. In: CAV. Lecture Notes in Computer Science, vol.\u00a01427, pp. 147\u2013158. Springer (1998)","DOI":"10.1007\/BFb0028741"},{"key":"25_CR8","doi-asserted-by":"crossref","unstructured":"Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244\u2013263 (1986)","DOI":"10.1145\/5397.5399"},{"key":"25_CR9","doi-asserted-by":"publisher","unstructured":"Clarke, E.M., Grumberg, O., Jha, S.: Verifying parameterized networks. ACM Trans. Program. Lang. Syst. 19(5), 726\u2013750 (1997). https:\/\/doi.org\/10.1145\/265943.265960","DOI":"10.1145\/265943.265960"},{"key":"25_CR10","doi-asserted-by":"publisher","unstructured":"Clarke, E.M., Jha, S., Enders, R., Filkorn, T.: Exploiting symmetry in temporal logic model checking. Formal Methods Syst. Des. 9(1\/2), 77\u2013104 (1996). https:\/\/doi.org\/10.1007\/BF00625969","DOI":"10.1007\/BF00625969"},{"key":"25_CR11","doi-asserted-by":"crossref","unstructured":"Donaldson, A.F., Miller, A.: Automatic symmetry detection for model checking using computational group theory. In: International Symposium on Formal Methods. pp. 481\u2013496. Springer (2005)","DOI":"10.1007\/11526841_32"},{"key":"25_CR12","doi-asserted-by":"crossref","unstructured":"Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pp. 995\u20131072. Elsevier and MIT Press (1990)","DOI":"10.1016\/B978-0-444-88074-1.50021-4"},{"key":"25_CR13","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Clarke, E.M.: Using branching time temporal logic to synthesize synchronization skeletons. Sci. Comput. Program. 2(3), 241\u2013266 (1982)","DOI":"10.1016\/0167-6423(83)90017-5"},{"key":"25_CR14","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Havlicek, J., Trefler, R.J.: Virtual symmetry reduction. In: LICS. pp. 121\u2013131. IEEE Computer Society (2000)","DOI":"10.1109\/LICS.2000.855761"},{"key":"25_CR15","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Kahlon, V.: Parameterized model checking of ring-based message passing systems. In: CSL. Lecture Notes in Computer Science, vol.\u00a03210, pp. 325\u2013339. Springer (2004)","DOI":"10.1007\/978-3-540-30124-0_26"},{"key":"25_CR16","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Namjoshi, K.S.: Reasoning about rings. In: POPL. pp. 85\u201394. ACM Press (1995)","DOI":"10.1145\/199448.199468"},{"key":"25_CR17","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Namjoshi, K.S.: On reasoning about rings. Int. J. Found. Comput. Sci. 14(4), 527\u2013550 (2003)","DOI":"10.1142\/S0129054103001881"},{"key":"25_CR18","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Formal Methods Syst. Des. 9(1\/2), 105\u2013131 (1996)","DOI":"10.1007\/BF00625970"},{"key":"25_CR19","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Sistla, A.P.: Utilizing symmetry when model-checking under fairness assumptions: An automata-theoretic approach. ACM Trans. Program. Lang. Syst. 19(4), 617\u2013638 (1997)","DOI":"10.1145\/262004.262008"},{"key":"25_CR20","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Trefler, R.J.: Model checking real-time properties of symmetric systems. In: MFCS. Lecture Notes in Computer Science, vol.\u00a01450, pp. 427\u2013436. Springer (1998)","DOI":"10.1007\/BFb0055792"},{"key":"25_CR21","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Trefler, R.J.: From asymmetry to full symmetry: New techniques for symmetry reduction in model checking. In: CHARME. Lecture Notes in Computer Science, vol.\u00a01703, pp. 142\u2013156. Springer (1999)","DOI":"10.1007\/3-540-48153-2_12"},{"key":"25_CR22","doi-asserted-by":"crossref","unstructured":"Emerson, E.A., Wahl, T.: Dynamic symmetry reduction. In: TACAS. Lecture Notes in Computer Science, vol.\u00a03440, pp. 382\u2013396. Springer (2005)","DOI":"10.1007\/978-3-540-31980-1_25"},{"key":"25_CR23","doi-asserted-by":"publisher","unstructured":"von Essen, C., Jobstmann, B.: Program repair without regret. Formal Methods Syst. Des. 47(1), 26\u201350 (2015). https:\/\/doi.org\/10.1007\/s10703-015-0223-6","DOI":"10.1007\/s10703-015-0223-6"},{"key":"25_CR24","doi-asserted-by":"publisher","unstructured":"German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675\u2013735 (1992). https:\/\/doi.org\/10.1145\/146637.146681","DOI":"10.1145\/146637.146681"},{"key":"25_CR25","doi-asserted-by":"publisher","unstructured":"Goues, C.L., Pradel, M., Roychoudhury, A.: Automated program repair. Commun. ACM 62(12), 56\u201365 (nov 2019). https:\/\/doi.org\/10.1145\/3318162","DOI":"10.1145\/3318162"},{"key":"25_CR26","doi-asserted-by":"publisher","unstructured":"Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Trans. Program. Lang. Syst. 16(3), 843\u2013871 (may 1994). https:\/\/doi.org\/10.1145\/177492.177725","DOI":"10.1145\/177492.177725"},{"key":"25_CR27","doi-asserted-by":"crossref","unstructured":"Isaacs, I.M.: Finite group theory, vol.\u00a092. American Mathematical Soc. (2008)","DOI":"10.1090\/gsm\/092"},{"key":"25_CR28","doi-asserted-by":"crossref","unstructured":"Isaacs, I.M.: Algebra: a graduate course, vol.\u00a0100. American Mathematical Soc. (2009)","DOI":"10.1090\/gsm\/100"},{"key":"25_CR29","doi-asserted-by":"crossref","unstructured":"Jobstmann, B., Griesmayer, A., Bloem, R.: Program repair as a game. In: CAV. pp. 226\u2013238. Springer-Verlag, Berlin, Heidelberg (2005)","DOI":"10.1007\/11513988_23"},{"key":"25_CR30","doi-asserted-by":"crossref","unstructured":"Namjoshi, K.S., Trefler, R.J.: Uncovering symmetries in irregular process networks. In: International Workshop on Verification, Model Checking, and Abstract Interpretation. pp. 496\u2013514. Springer (2013)","DOI":"10.1007\/978-3-642-35873-9_29"},{"key":"25_CR31","unstructured":"Serre, J.P.: Finite groups: an introduction. International Press Somerville, MA (2016)"},{"key":"25_CR32","doi-asserted-by":"crossref","unstructured":"Staber, S., Jobstmann, B., Bloem, R.: Finding and fixing faults. In: CHARME \u201905. pp. 35\u201349. Springer-Verlag, Berlin, Heidelberg (2005), springer LNCS no. 3725","DOI":"10.1007\/11560548_6"}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-30829-1_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T22:42:29Z","timestamp":1729291349000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-30829-1_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031308284","9783031308291"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-30829-1_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"21 April 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FoSSaCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Foundations of Software Science and Computation Structures","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 April 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 April 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fossacs2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2023\/fossacs","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":"85","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":"26","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":"0","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":"31% - 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":"3.1","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":"10","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)"}}]}}