Dinur, Irit, Goldreich, Oded and Gur, Tom (2019) Every set in P is strongly testable under a suitable encoding. In: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Published in: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019), 124 30:1-30:17. ISBN 9783959770958. ISSN 1868-8969. doi:10.4230/LIPIcs.ITCS.2019.30

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Abstract

We show that every set in P is strongly testable under a suitable encoding. By "strongly testable" we mean having a (proximity oblivious) tester that makes a constant number of queries and rejects with probability that is proportional to the distance of the tested object from the property. By a "suitable encoding" we mean one that is polynomial-time computable and invertible. This result stands in contrast to the known fact that some sets in P are extremely hard to test, providing another demonstration of the crucial role of representation in the context of property testing. The testing result is proved by showing that any set in P has a strong canonical PCP, where canonical means that (for yes-instances) there exists a single proof that is accepted with probability 1 by the system, whereas all other potential proofs are rejected with probability proportional to their distance from this proof. In fact, we show that UP equals the class of sets having strong canonical PCPs (of logarithmic randomness), whereas the class of sets having strong canonical PCPs with polynomial proof length equals "unambiguous- MA". Actually, for the testing result, we use a PCP-of-Proximity version of the foregoing notion and an analogous positive result (i.e., strong canonical PCPPs of logarithmic randomness for any set in UP).

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH):	Data encryption (Computer science), Computer security, Cryptography
Series Name:	Leibniz International Proceedings in Informatics (LIPIcs)
Journal or Publication Title:	10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Publisher:	Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of Publication:	Dagstuhl, Germany
ISBN:	9783959770958
ISSN:	1868-8969
Official Date:	2019
Dates:	Date Event 2019 Published 31 October 2018 Accepted
Volume:	124
Page Range:	30:1-30:17
DOI:	10.4230/LIPIcs.ITCS.2019.30
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID 772839 European Research Council http://viaf.org/viaf/130022607 UNSPECIFIED Israel Science Foundation http://dx.doi.org/10.13039/501100003977 Center for Long-Term Cybersecurity University of California Berkeley http://dx.doi.org/10.13039/100006978
Conference Paper Type:	Paper
Title of Event:	10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Type of Event:	Conference
Related URLs:	Organisation

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