{"id":158386,"date":"2009-10-25T00:00:00","date_gmt":"2009-10-25T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/a-parallel-repetition-theorem-for-any-interactive-argument\/"},"modified":"2018-10-16T19:58:32","modified_gmt":"2018-10-17T02:58:32","slug":"a-parallel-repetition-theorem-for-any-interactive-argument","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/a-parallel-repetition-theorem-for-any-interactive-argument\/","title":{"rendered":"A Parallel Repetition Theorem for Any Interactive Argument"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The question whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols &#8211; Bellare, Impagliazzo and Naor [FOCS &#8217;97], and public-coin protocols &#8211; H\u00e5stad, Pass, Pietrzak and Wikstr\u00c4om [Manuscript &#8217;08]), Bellare et. al gave example of interactive arguments for which parallel repetition does not reduce the soundness error at all. We show that by slightly modifying any interactive argument, in a way that preserves its completeness and only slightly deteriorates its soundness, we get a protocol for which parallel repetition does reduce the error at a weak exponential rate. In this modified version, the verifier flips at the beginning of each round an (1 &#8211; (1\/4m), 1\/4m) biased coin (i.e., 1 is tossed with probability 1\/4m), where m is the round complexity of the (original) protocol. If the coin is one, the verifier halts the interaction and accepts, otherwise it sends the same message that the original verifier would. At the end of the protocol (if reached), the verifier accepts if and only if the original verifier would.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The question whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols &#8211; Bellare, Impagliazzo and Naor [FOCS &#8217;97], [&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":"iftach"}],"msr_publishername":"Association for Computing Machinery, Inc.","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"FOCS 2009","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2009-144","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2007 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and\/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or permissions@acm.org. The definitive version of this paper can be found at ACM's Digital Library --http:\/\/www.acm.org\/dl\/.","msr_conference_name":"","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":"2009-10-25","msr_highlight_text":"","msr_notes":"FOCS 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