{"id":152972,"date":"2006-06-01T00:00:00","date_gmt":"2006-06-01T00:00:00","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/msr-research-item\/the-bit-vector-constraint\/"},"modified":"2018-10-16T20:24:46","modified_gmt":"2018-10-17T03:24:46","slug":"the-bit-vector-constraint","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/the-bit-vector-constraint\/","title":{"rendered":"The bit-vector Constraint"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Some applications require to reason on particular bits of an integer value, and to express the fact that &#8220;the number X is encoded in binary by the vector of Boolean variables [x<sub>n<\/sub>, &#8230;, x<sub>0<\/sub>]&#8221;. The natural way to encode this is using a linear constraint. We show that bound propagation on this constraint has intriguing properties: it is complete in the sense that the bounds of the variable x<sub>i<\/sub> (i in 0 .. n) are tightly reduced; on the other hand, the interval of values for X is in general not optimally reduced: it can be up to twice as large as the optimal. We show that a simple mechanism allows the reasoning to be complete on X.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Some applications require to reason on particular bits of an integer value, and to express the fact that &#8220;the number X is encoded in binary by the vector of Boolean variables [xn, &#8230;, x0]&#8221;. The natural way to encode this is using a linear constraint. We show that bound propagation on this constraint has intriguing [&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":null,"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-TR-2006-86","msr_organization":"","msr_pages_string":"7","msr_page_range_start":"7","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Claude-Guy Quimper","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"Microsoft Research","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":"2006-06-01","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":2006,"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":[13555],"msr-publication-type":[193718],"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-152972","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-search-information-retrieval","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2006-06-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"7","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"MSR-TR-2006-86","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":"209039","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"tr-2006-86.pdf","viewUrl":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/02\/tr-2006-86.pdf","id":209039,"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":[],"msr-author-ordering":[{"type":"user_nicename","value":"youssefh","user_id":35047,"rest_url":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=youssefh"},{"type":"user_nicename","value":"lucasb","user_id":32744,"rest_url":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=lucasb"},{"type":"text","value":"Claude-Guy Quimper","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"techreport","related_content":[],"_links":{"self":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/152972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/152972\/revisions"}],"predecessor-version":[{"id":527376,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/152972\/revisions\/527376"}],"wp:attachment":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=152972"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=152972"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=152972"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=152972"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=152972"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=152972"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=152972"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=152972"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=152972"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=152972"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=152972"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=152972"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=152972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}