Debates with small transparent quantum verifiers
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an otherwise classical constant-space verifier raises the class of de...
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| creator | Yakaryilmaz, Abuzer Say, A. C. Cem Demirci, H. Gökalp |
| description | We study a model where two opposing provers debate over the membership status
of a given string in a language, trying to convince a weak verifier whose coins
are visible to all. We show that the incorporation of just two qubits to an
otherwise classical constant-space verifier raises the class of debatable
languages from at most $\mathsf{NP}$ to the collection of all Turing-decidable
languages (recursive languages). When the verifier is further constrained to
make the correct decision with probability 1, the corresponding class goes up
from the regular languages up to at least $\mathsf{E}$. We also show that the
quantum model outperforms its classical counterpart when restricted to run in
polynomial time, and demonstrate some non-context-free languages which have
such short debates with quantum verifiers. |
| doi_str_mv | 10.48550/arxiv.1405.1655 |
| format | Article |
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of a given string in a language, trying to convince a weak verifier whose coins
are visible to all. We show that the incorporation of just two qubits to an
otherwise classical constant-space verifier raises the class of debatable
languages from at most $\mathsf{NP}$ to the collection of all Turing-decidable
languages (recursive languages). When the verifier is further constrained to
make the correct decision with probability 1, the corresponding class goes up
from the regular languages up to at least $\mathsf{E}$. We also show that the
quantum model outperforms its classical counterpart when restricted to run in
polynomial time, and demonstrate some non-context-free languages which have
such short debates with quantum verifiers.</description><identifier>DOI: 10.48550/arxiv.1405.1655</identifier><language>eng</language><subject>Computer Science - Computational Complexity ; Computer Science - Formal Languages and Automata Theory ; Physics - Quantum Physics</subject><creationdate>2014-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1405.1655$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1405.1655$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Yakaryilmaz, Abuzer</creatorcontrib><creatorcontrib>Say, A. C. Cem</creatorcontrib><creatorcontrib>Demirci, H. Gökalp</creatorcontrib><title>Debates with small transparent quantum verifiers</title><description>We study a model where two opposing provers debate over the membership status
of a given string in a language, trying to convince a weak verifier whose coins
are visible to all. We show that the incorporation of just two qubits to an
otherwise classical constant-space verifier raises the class of debatable
languages from at most $\mathsf{NP}$ to the collection of all Turing-decidable
languages (recursive languages). When the verifier is further constrained to
make the correct decision with probability 1, the corresponding class goes up
from the regular languages up to at least $\mathsf{E}$. We also show that the
quantum model outperforms its classical counterpart when restricted to run in
polynomial time, and demonstrate some non-context-free languages which have
such short debates with quantum verifiers.</description><subject>Computer Science - Computational Complexity</subject><subject>Computer Science - Formal Languages and Automata Theory</subject><subject>Physics - Quantum Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr1OwzAUQGEvHVDanQn5BRL8E9s3Y1UoIFXqkj26SW-EpSRqbTfA27cBprMdfYw9SlGUYIx4xvDt50KWwhTSGvPAxAu1mCjyL58-eRxxGHgKOMUzBpoSv1xxSteRzxR87ynENVv1OETa_Ddj9f613r3nh-Pbx257yPH-za0GUTpVucpWwhEgoLRKKnU6Uee6voVWg-xdZ1zpLAhNUHUgrCSFrZJOZ-zpb_srbs7Bjxh-mkXeLHJ9A87FPP8</recordid><startdate>20140507</startdate><enddate>20140507</enddate><creator>Yakaryilmaz, Abuzer</creator><creator>Say, A. C. Cem</creator><creator>Demirci, H. Gökalp</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20140507</creationdate><title>Debates with small transparent quantum verifiers</title><author>Yakaryilmaz, Abuzer ; Say, A. C. Cem ; Demirci, H. Gökalp</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a655-63804729796907e8a8a162122ddec7cfb8b381f7c57476803e89c8061e2ab2173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Computer Science - Computational Complexity</topic><topic>Computer Science - Formal Languages and Automata Theory</topic><topic>Physics - Quantum Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Yakaryilmaz, Abuzer</creatorcontrib><creatorcontrib>Say, A. C. Cem</creatorcontrib><creatorcontrib>Demirci, H. Gökalp</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yakaryilmaz, Abuzer</au><au>Say, A. C. Cem</au><au>Demirci, H. Gökalp</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Debates with small transparent quantum verifiers</atitle><date>2014-05-07</date><risdate>2014</risdate><abstract>We study a model where two opposing provers debate over the membership status
of a given string in a language, trying to convince a weak verifier whose coins
are visible to all. We show that the incorporation of just two qubits to an
otherwise classical constant-space verifier raises the class of debatable
languages from at most $\mathsf{NP}$ to the collection of all Turing-decidable
languages (recursive languages). When the verifier is further constrained to
make the correct decision with probability 1, the corresponding class goes up
from the regular languages up to at least $\mathsf{E}$. We also show that the
quantum model outperforms its classical counterpart when restricted to run in
polynomial time, and demonstrate some non-context-free languages which have
such short debates with quantum verifiers.</abstract><doi>10.48550/arxiv.1405.1655</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Complexity Computer Science - Formal Languages and Automata Theory Physics - Quantum Physics |
| title | Debates with small transparent quantum verifiers |
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