{"id":157341,"date":"2009-03-01T00:00:00","date_gmt":"2009-03-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/complexity-and-algorithms-for-monomial-and-clausal-predicate-abstraction\/"},"modified":"2018-10-16T21:59:44","modified_gmt":"2018-10-17T04:59:44","slug":"complexity-and-algorithms-for-monomial-and-clausal-predicate-abstraction","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/complexity-and-algorithms-for-monomial-and-clausal-predicate-abstraction\/","title":{"rendered":"Complexity and algorithms for monomial and clausal predicate abstraction"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this paper, we investigate the asymptotic complexity of various predicate abstraction problems relative to the complexity of checking an annotated program in an assertion logic. Unlike previous approaches, we pose the predicate abstraction problem as a decision problem, instead of the traditional inference problem. For assertion logics closed under weakest precondition and Boolean connectives, we show two restrictions of the predicate abstraction problem where the problem is no worse than checking an annotated program! The restrictions correspond to the case of monomial and clausal abstraction. For these restrictions, we show a symbolic encoding that reduces the predicate abstraction problem to checking the satisfiability of a single formula whose size is polynomial in the size of the program and the set of predicates. We also provide a new iterative algorithm for solving the clausal abstraction problem that can be seen as the dual of the Houdini algorithm for solving the monomial abstraction problem.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we investigate the asymptotic complexity of various predicate abstraction problems relative to the complexity of checking an annotated program in an assertion logic. Unlike previous approaches, we pose the predicate abstraction problem as a decision problem, instead of the traditional inference problem. For assertion logics closed under weakest precondition and Boolean connectives, [&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":"shuvendu"},{"type":"user_nicename","value":"qadeer"}],"msr_publishername":"Springer Verlag","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"International Conference on Automated Deduction (CADE '09)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2009-2012","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Conference on Automated Deduction (CADE '09)","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":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2009-03-01","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":2009,"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":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561,13560],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-157341","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"Springer Verlag","msr_edition":"International Conference on Automated Deduction (CADE '09)","msr_affiliation":"","msr_published_date":"2009-03-01","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-TR-2009-2012","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":"207781","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"paper.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/paper-89.pdf","id":207781,"label_id":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":[{"id":207781,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/paper-89.pdf"}],"msr-author-ordering":[{"type":"user_nicename","value":"shuvendu","user_id":33640,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=shuvendu"},{"type":"user_nicename","value":"qadeer","user_id":33294,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=qadeer"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[170008],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":170008,"post_title":"HAVOC","post_name":"havoc","post_type":"msr-project","post_date":"2008-11-25 22:51:13","post_modified":"2017-09-19 17:00:32","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/havoc\/","post_excerpt":"HAVOC is a tool for specifying and checking properties of systems software written in C, in the presence of pointer manipulations, unsafe casts and dynamic memory allocation. The assertion logic of HAVOC allows the expression of properties of linked lists and arrays. The main challenge addressed by the tool are (1) tradeoff between expressiveness of the assertion logic and its computational efficiency, (2) generic inference techniques to relieve users of annotation burden for large modules.","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/170008"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/157341","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\/157341\/revisions"}],"predecessor-version":[{"id":541008,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/157341\/revisions\/541008"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=157341"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=157341"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=157341"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=157341"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=157341"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=157341"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=157341"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=157341"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=157341"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=157341"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=157341"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=157341"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=157341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}