{"id":360482,"date":"2017-02-01T15:26:30","date_gmt":"2017-02-01T23:26:30","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=360482"},"modified":"2018-10-16T20:04:02","modified_gmt":"2018-10-17T03:04:02","slug":"definability-constant-depth-polynomial-size-circuits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/definability-constant-depth-polynomial-size-circuits\/","title":{"rendered":"Definability by Constant-depth Polynomial-size Circuits"},"content":{"rendered":"

We investigate the expressive power of constant-depth polynomial-size circuit models. In particular, we construct a circuit model whose expressive power is precisely that of first-order logic.<\/p>\n","protected":false},"excerpt":{"rendered":"

We investigate the expressive power of constant-depth polynomial-size circuit models. In particular, we construct a circuit model whose expressive power is precisely that of first-order logic.<\/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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13560],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-360482","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"1986-04-08","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"216-240","msr_chapter":"","msr_isbn":"","msr_journal":"Information and Control","msr_volume":"70","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":"http:\/\/web.eecs.umich.edu\/~gurevich\/Opera\/67.pdf","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"http:\/\/web.eecs.umich.edu\/~gurevich\/Opera\/67.pdf","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/web.eecs.umich.edu\/~gurevich\/Opera\/67.pdf"}],"msr-author-ordering":[{"type":"text","value":"L. 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