{"id":1143239,"date":"2025-06-27T13:04:18","date_gmt":"2025-06-27T20:04:18","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=1143239"},"modified":"2025-06-27T13:05:54","modified_gmt":"2025-06-27T20:05:54","slug":"arithmetic-solving-in-z3","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/arithmetic-solving-in-z3\/","title":{"rendered":"Arithmetic Solving in Z3"},"content":{"rendered":"<section lang=\"en\" aria-labelledby=\"Abs1\" data-title=\"Abstract\">\n<div id=\"Abs1-section\" class=\"c-article-section\">\n<div id=\"Abs1-content\" class=\"c-article-section__content\">\n<p>The theory of arithmetic is integral to many uses of SMT solvers. Z3 has implemented native solvers for arithmetic reasoning since its first release. We present a full re-implementation of Z3\u2019s original arithmetic solver. It is based on substantial experiences from user feedback, engineering and experimentation. While providing a comprehensive overview of the main components we emphasize selected new insights we arrived at while developing and testing the solver.<\/p>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The theory of arithmetic is integral to many uses of SMT solvers. Z3 has implemented native solvers for arithmetic reasoning since its first release. We present a full re-implementation of Z3\u2019s original arithmetic solver. It is based on substantial experiences from user feedback, engineering and experimentation. While providing a comprehensive overview of the main components [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"user_nicename","value":"Nikolaj Bj\u00f8rner","user_id":"33067"},{"type":"user_nicename","value":"Lev Nachmanson","user_id":"32653"}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"26","msr_page_range_end":"41","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Computer Aided Verification (CAV 2024)","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":null,"msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2024-7-26","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":null,"footnotes":""},"msr-research-highlight":[],"research-area":[13561,13546,13560],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[269148,269142],"msr-field-of-study":[246691],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-1143239","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-research-area-programming-languages-software-engineering","msr-locale-en_us","msr-post-option-approved-for-river","msr-post-option-include-in-river","msr-field-of-study-computer-science"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2024-7-26","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-031-65627-9_2","label_id":"243109","label":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"Nikolaj Bj\u00f8rner","user_id":33067,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Nikolaj Bj\u00f8rner"},{"type":"user_nicename","value":"Lev Nachmanson","user_id":32653,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Lev Nachmanson"}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1143239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1143239\/revisions"}],"predecessor-version":[{"id":1143243,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1143239\/revisions\/1143243"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=1143239"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=1143239"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=1143239"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=1143239"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=1143239"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=1143239"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=1143239"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=1143239"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=1143239"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=1143239"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=1143239"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=1143239"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=1143239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}