{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T20:43:18Z","timestamp":1773348198126,"version":"3.50.1"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031634970","type":"print"},{"value":"9783031634987","type":"electronic"}],"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":[[2024,7,1]],"date-time":"2024-07-01T00:00:00Z","timestamp":1719792000000},"content-version":"vor","delay-in-days":182,"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>\n          <jats:p>This system description introduces an enhancement to the <jats:sc>Yices2<\/jats:sc> SMT solver, enabling it to reason over non-linear polynomial systems over finite fields. Our reasoning approach fits into the model-constructing satisfiability (MCSat) framework and is based on zero decomposition techniques, which find finite basis explanations for theory conflicts over finite fields. As the MCSat solver within <jats:sc>Yices2<\/jats:sc> can support (and combine) several theories via theory plugins, we implemented our reasoning approach as a new plugin for finite fields and extended <jats:sc>Yices2<\/jats:sc> \u2019s frontend to parse finite field problems, making our implementation the first MCSat-based reasoning engine for finite fields. We present its evaluation on finite field benchmarks, comparing it against <jats:sc>cvc5<\/jats:sc>. Additionally, our work leverages the modular architecture of the MCSat solver in <jats:sc>Yices2<\/jats:sc> to provide a foundation for the rapid implementation of further reasoning techniques for this theory.<\/jats:p>","DOI":"10.1007\/978-3-031-63498-7_23","type":"book-chapter","created":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T19:01:44Z","timestamp":1719774104000},"page":"386-395","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["MCSat-Based Finite Field Reasoning in\u00a0the\u00a0Yices2 SMT Solver (Short Paper)"],"prefix":"10.1007","author":[{"given":"Thomas","family":"Hader","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5645-0292","authenticated-orcid":false,"given":"Daniela","family":"Kaufmann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7791-9021","authenticated-orcid":false,"given":"Ahmed","family":"Irfan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2112-7284","authenticated-orcid":false,"given":"St\u00e9phane","family":"Graham-Lengrand","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8299-2714","authenticated-orcid":false,"given":"Laura","family":"Kov\u00e1cs","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,1]]},"reference":[{"key":"23_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/978-3-030-99524-9_24","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"H Barbosa","year":"2022","unstructured":"Barbosa, H., et al.: cvc5: a versatile and industrial-strength SMT solver. In: TACAS 2022. LNCS, vol. 13243, pp. 415\u2013442. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99524-9_24"},{"key":"23_CR2","unstructured":"Barrett, C., Fontaine, P., Tinelli, C.: The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org (2016)"},{"key":"23_CR3","doi-asserted-by":"publisher","unstructured":"Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability - Second Edition, Frontiers in Artificial Intelligence and Applications, vol.\u00a0336, pp. 1267\u20131329. IOS Press (2021). https:\/\/doi.org\/10.3233\/FAIA201017, https:\/\/doi.org\/10.3233\/FAIA201017","DOI":"10.3233\/FAIA201017"},{"key":"23_CR4","doi-asserted-by":"publisher","unstructured":"Buchberger, B.: Bruno Buchberger\u2019s PhD Thesis 1965: an algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. J. Symbol. Comput. 41(3-4), 475\u2013511 (2006). https:\/\/doi.org\/10.1016\/J.JSC.2005.09.007","DOI":"10.1016\/J.JSC.2005.09.007"},{"key":"23_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1007\/978-3-319-08867-9_49","volume-title":"Computer Aided Verification","author":"B Dutertre","year":"2014","unstructured":"Dutertre, B.: Yices\u00a02.2. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 737\u2013744. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-08867-9_49"},{"key":"23_CR6","unstructured":"Dutertre, B., Goel, A., Graham-Lengrand, S., Irfan, A., Jovanovic, D., Mason, I.A.: Yices 2 in SMT-COMP 2023 (2023)"},{"issue":"1","key":"23_CR7","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/0218012","volume":"18","author":"S Goldwasser","year":"1989","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186\u2013208 (1989). https:\/\/doi.org\/10.1137\/0218012","journal-title":"SIAM J. Comput."},{"key":"23_CR8","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/978-3-030-51074-9_7","volume-title":"Automated Reasoning","author":"S Graham-Lengrand","year":"2020","unstructured":"Graham-Lengrand, S., Jovanovi\u0107, D., Dutertre, B.: Solving Bitvectors with MCSAT: explanations from bits and pieces. In: Peltier, N., Sofronie-Stokkermans, V. (eds.) IJCAR 2020. LNCS (LNAI), vol. 12166, pp. 103\u2013121. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-51074-9_7"},{"key":"23_CR9","doi-asserted-by":"publisher","unstructured":"Hader, T., Kaufmann, D., Kov\u00e1cs, L.: SMT solving over finite field arithmetic. In: Piskac, R., Voronkov, A. (eds.) Intl. Conf. on Logic for Programming, Artificial Intelligence and Reasoning (LPAR). EPiC Series in Computing, vol.\u00a094, pp. 238\u2013256. EasyChair (2023). https:\/\/doi.org\/10.29007\/4N6W, https:\/\/doi.org\/10.29007\/4n6w","DOI":"10.29007\/4N6W"},{"key":"23_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1007\/978-3-319-52234-0_18","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"D Jovanovi\u0107","year":"2017","unstructured":"Jovanovi\u0107, D.: Solving nonlinear integer arithmetic with MCSAT. In: Bouajjani, A., Monniaux, D. (eds.) VMCAI 2017. LNCS, vol. 10145, pp. 330\u2013346. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-52234-0_18"},{"key":"23_CR11","doi-asserted-by":"publisher","unstructured":"Jovanovic, D., Barrett, C., de\u00a0Moura, L.: The design and implementation of the model constructing satisfiability calculus. In: International Conference on Formal Methods in Computer-Aided Design (FMCAD), pp. 173\u2013180. IEEE (2013).https:\/\/doi.org\/10.1109\/FMCAD.2013.7027033","DOI":"10.1109\/FMCAD.2013.7027033"},{"key":"23_CR12","unstructured":"Jovanovic, D., Dutertre, B.: Libpoly: a library for reasoning about polynomials. In: Brain, M., Hadarean, L. (eds.) Intl. Workshop on Satisfiability Modulo Theories (SMT). CEUR Workshop Proceedings, vol.\u00a01889, pp. 28\u201339. CEUR-WS.org (2017). https:\/\/ceur-ws.org\/Vol-1889\/paper3.pdf"},{"key":"23_CR13","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/978-3-642-31365-3_27","volume-title":"Automated Reasoning","author":"D Jovanovi\u0107","year":"2012","unstructured":"Jovanovi\u0107, D., de Moura, L.: Solving non-linear arithmetic. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 339\u2013354. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-31365-3_27"},{"key":"23_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-35873-9_1","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"L de Moura","year":"2013","unstructured":"de Moura, L., Jovanovi\u0107, D.: A model-constructing satisfiability calculus. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 1\u201312. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-35873-9_1"},{"issue":"9","key":"23_CR15","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1145\/1995376.1995394","volume":"54","author":"LM de Moura","year":"2011","unstructured":"de Moura, L.M., Bj\u00f8rner, N.S.: Satisfiability modulo theories: introduction and applications. Commun. ACM 54(9), 69\u201377 (2011)","journal-title":"Commun. ACM"},{"key":"23_CR16","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-540-32275-7_3","volume-title":"Logic for Programming, Artificial Intelligence, and Reasoning","author":"R Nieuwenhuis","year":"2005","unstructured":"Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Abstract DPLL and abstract DPLL modulo theories. In: Baader, F., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3452, pp. 36\u201350. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/978-3-540-32275-7_3"},{"key":"23_CR17","doi-asserted-by":"publisher","unstructured":"Ozdemir, A., Kremer, G., Tinelli, C., Barrett, C.W.: Satisfiability modulo finite fields. In: International Conference on Computer Aided Verification (CAV), Part\u00a0II. LNCS, vol. 13965, pp. 163\u2013186. Springer (2023).https:\/\/doi.org\/10.1007\/978-3-031-37703-7_8","DOI":"10.1007\/978-3-031-37703-7_8"},{"key":"23_CR18","doi-asserted-by":"publisher","unstructured":"Ozdemir, A., Wahby, R.S., Brown, F., Barrett, C.W.: Bounded verification for finite-field-blasting - in a compiler for zero knowledge proofs. In: Enea, C., Lal, A. (eds.) International Conference on Computer Aided Verification (CAV), Part\u00a0III. LNCS, vol. 13966, pp. 154\u2013175. Springer (2023).https:\/\/doi.org\/10.1007\/978-3-031-37709-9_8","DOI":"10.1007\/978-3-031-37709-9_8"},{"key":"23_CR19","unstructured":"Szabo, N.: Smart Contracts: Building Blocks for Digital Markets (1996). http:\/\/www.fon.hum.uva.nl"},{"key":"23_CR20","unstructured":"Wang, D.: Elimination Methods. Springer Science & Business Media (2001)"}],"container-title":["Lecture Notes in Computer Science","Automated Reasoning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-63498-7_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T18:17:34Z","timestamp":1747592254000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-63498-7_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031634970","9783031634987"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-63498-7_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"1 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"IJCAR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Joint Conference on Automated Reasoning","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Nancy","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":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ijcar2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/merz.gitlabpages.inria.fr\/2024-ijcar\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}