{"id":667485,"date":"2020-06-16T11:14:15","date_gmt":"2020-06-16T18:14:15","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=667485"},"modified":"2020-06-26T10:06:29","modified_gmt":"2020-06-26T17:06:29","slug":"no-signaling-proofs-with-o%e2%88%9alog-n-provers-is-in-pspace","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/no-signaling-proofs-with-o%e2%88%9alog-n-provers-is-in-pspace\/","title":{"rendered":"Non-Signaling Proofs with O(\u221alog n) Provers is in PSPACE"},"content":{"rendered":"<p>Non-signaling proofs, motivated by quantum computation, have found applications in cryptography and hardness of approximation. An important open problem is characterizing the power of no-signaling proofs. It is known that 2-prover no-signaling proofs are characterized by PSPACE, and that no-signaling proofs with\u00a0<em>poly<\/em>(<em>n<\/em>)-provers are characterized by EXP. However, the power of\u00a0<em>k<\/em>-prover no-signaling proofs, for\u00a0<em>2<\/em><<em>k<\/em><<em>poly<\/em>(<em>n<\/em>)\u00a0remained an open problem.<\/p>\n<p>We show that\u00a0<em>k<\/em>-prover no-signaling proofs (with negligible soundness) for\u00a0<em>k<\/em>=<em>O<\/em>(\u221alog<em>n<\/em>)\u00a0are contained in PSPACE. We prove this via two different routes that are of independent interest. In both routes we consider a relaxation of no-signaling called sub-no-signaling. Our main technical contribution (which is used in both our proofs) is a reduction showing how to convert any sub-no-signaling strategy with value at least\u00a01\u22122<sup>\u2212\u03a9(k2)<\/sup>\u00a0into a no-signaling one with value at least\u00a02<sup>\u2212O(k2)<\/sup>.<\/p>\n<p>In the first route, we show that the classical prover reduction method for converting k-prover games into 2-prover games carries over to the no-signaling setting with the following loss in soundness: if a k-player game has value less than 2<sup>\u2212ck2<\/sup>\u00a0(for some constant~c>0), then the corresponding 2-prover game has value at most\u00a01\u22122<em><sup>dk2<\/sup><\/em>\u00a0(for some constant~d>0). In the second route we show that the value of a sub-no-signaling game can be approximated in space that is polynomial in the communication complexity and exponential in the number of provers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Non-signaling proofs, motivated by quantum computation, have found applications in cryptography and hardness of approximation. An important open problem is characterizing the power of no-signaling proofs. It is known that 2-prover no-signaling proofs are characterized by PSPACE, and that no-signaling proofs with\u00a0poly(n)-provers are characterized by EXP. However, the power of\u00a0k-prover no-signaling proofs, for\u00a020). In the [&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_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"STOC 2020","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":"2020-6-1","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"http:\/\/acm-stoc.org\/stoc2020\/","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":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13546,243138],"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-667485","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2020-6-1","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:\/\/arxiv.org\/abs\/1910.02590","label_id":"243109","label":0},{"type":"doi","viewUrl":"false","id":"false","title":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3357713.3384246","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":"text","value":"Dhiraj Holden","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Yael Tauman Kalai","user_id":34951,"rest_url":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Yael Tauman Kalai"}],"msr_impact_theme":[],"msr_research_lab":[199563],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/667485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":4,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/667485\/revisions"}],"predecessor-version":[{"id":669972,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/667485\/revisions\/669972"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=667485"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=667485"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=667485"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=667485"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=667485"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=667485"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=667485"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=667485"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=667485"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=667485"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=667485"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=667485"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=667485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}