FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1699655904> ?p ?o ?g. }

• W1699655904 endingPage "320" @default.
• W1699655904 startingPage "309" @default.
• W1699655904 abstract "A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show that a deterministic black-box identity testing algorithm for (high-degree) univariate polynomials would imply a lower bound on the arithmetic complexity of the permanent. The lower bounds that are known to follow from derandomization of (low-degree) multivariate identity testing are weaker. To obtain a lower bound for the permanent it would be su-cient to derandomize identity testing for polynomials of a very speciflc norm: sums of products of sparse polynomials with sparse coe-cients. This observation leads to new versions of the Shub-Smale ?-conjecture on integer roots of univariate polynomials. In particular, we show that a lower bound for the permanent would follow if one could give a polynomial upper bound on the number of real roots of sums of products of sparse polynomials (Descartes' rule of signs gives such a bound for sparse polynomials and products thereof). In fact the same lower bound would follow even if one could only prove a slightly superpolynomial upper bound on the number of real roots. This is a consequence of a new result on reduction to depth 4 for arithmetic circuits which we establish in a companion paper. We also show that an even weaker bound on the number of real roots would su-ce to obtain a lower bound on the size of depth 4 circuits computing the permanent. These results suggest the intriguing possibility that tools from real analysis might be brought to bear on a longstanding open problem: what is the arithmetic complexity of the permanent polynomial?" @default.
• W1699655904 created "2016-06-24" @default.
• W1699655904 creator A5048679959 @default.
• W1699655904 date "2010-04-28" @default.
• W1699655904 modified "2023-09-25" @default.
• W1699655904 title "Shallow Circuits with High-Powered Inputs" @default.
• W1699655904 cites W1489417824 @default.
• W1699655904 cites W1503731768 @default.
• W1699655904 cites W1508725836 @default.
• W1699655904 cites W1576854535 @default.
• W1699655904 cites W1611937190 @default.
• W1699655904 cites W1760941220 @default.
• W1699655904 cites W1970085887 @default.
• W1699655904 cites W1991614107 @default.
• W1699655904 cites W2016576580 @default.
• W1699655904 cites W2026036943 @default.
• W1699655904 cites W2033323875 @default.
• W1699655904 cites W2040721698 @default.
• W1699655904 cites W2044413922 @default.
• W1699655904 cites W2082560626 @default.
• W1699655904 cites W2091278332 @default.
• W1699655904 cites W2100272829 @default.
• W1699655904 cites W2109639888 @default.
• W1699655904 cites W2118951952 @default.
• W1699655904 cites W2123100908 @default.
• W1699655904 cites W2128510017 @default.
• W1699655904 cites W2153575169 @default.
• W1699655904 cites W2170831059 @default.
• W1699655904 cites W2963534336 @default.
• W1699655904 cites W412941528 @default.
• W1699655904 hasPublicationYear "2010" @default.
• W1699655904 type Work @default.
• W1699655904 sameAs 1699655904 @default.
• W1699655904 citedByCount "10" @default.
• W1699655904 countsByYear W16996559042012 @default.
• W1699655904 countsByYear W16996559042013 @default.
• W1699655904 countsByYear W16996559042019 @default.
• W1699655904 crossrefType "proceedings-article" @default.
• W1699655904 hasAuthorship W1699655904A5048679959 @default.
• W1699655904 hasConcept C105795698 @default.
• W1699655904 hasConcept C114614502 @default.
• W1699655904 hasConcept C118615104 @default.
• W1699655904 hasConcept C121332964 @default.
• W1699655904 hasConcept C134306372 @default.
• W1699655904 hasConcept C155920423 @default.
• W1699655904 hasConcept C161584116 @default.
• W1699655904 hasConcept C199163554 @default.
• W1699655904 hasConcept C199360897 @default.
• W1699655904 hasConcept C24890656 @default.
• W1699655904 hasConcept C2775997480 @default.
• W1699655904 hasConcept C2778355321 @default.
• W1699655904 hasConcept C2780990831 @default.
• W1699655904 hasConcept C33923547 @default.
• W1699655904 hasConcept C41008148 @default.
• W1699655904 hasConcept C77553402 @default.
• W1699655904 hasConcept C83581934 @default.
• W1699655904 hasConcept C90119067 @default.
• W1699655904 hasConcept C94375191 @default.
• W1699655904 hasConcept C97137487 @default.
• W1699655904 hasConceptScore W1699655904C105795698 @default.
• W1699655904 hasConceptScore W1699655904C114614502 @default.
• W1699655904 hasConceptScore W1699655904C118615104 @default.
• W1699655904 hasConceptScore W1699655904C121332964 @default.
• W1699655904 hasConceptScore W1699655904C134306372 @default.
• W1699655904 hasConceptScore W1699655904C155920423 @default.
• W1699655904 hasConceptScore W1699655904C161584116 @default.
• W1699655904 hasConceptScore W1699655904C199163554 @default.
• W1699655904 hasConceptScore W1699655904C199360897 @default.
• W1699655904 hasConceptScore W1699655904C24890656 @default.
• W1699655904 hasConceptScore W1699655904C2775997480 @default.
• W1699655904 hasConceptScore W1699655904C2778355321 @default.
• W1699655904 hasConceptScore W1699655904C2780990831 @default.
• W1699655904 hasConceptScore W1699655904C33923547 @default.
• W1699655904 hasConceptScore W1699655904C41008148 @default.
• W1699655904 hasConceptScore W1699655904C77553402 @default.
• W1699655904 hasConceptScore W1699655904C83581934 @default.
• W1699655904 hasConceptScore W1699655904C90119067 @default.
• W1699655904 hasConceptScore W1699655904C94375191 @default.
• W1699655904 hasConceptScore W1699655904C97137487 @default.
• W1699655904 hasLocation W16996559041 @default.
• W1699655904 hasOpenAccess W1699655904 @default.
• W1699655904 hasPrimaryLocation W16996559041 @default.
• W1699655904 hasRelatedWork W1503731768 @default.
• W1699655904 hasRelatedWork W1576854535 @default.
• W1699655904 hasRelatedWork W1580127749 @default.
• W1699655904 hasRelatedWork W1599026900 @default.
• W1699655904 hasRelatedWork W1968245619 @default.
• W1699655904 hasRelatedWork W1974827405 @default.
• W1699655904 hasRelatedWork W1998853590 @default.
• W1699655904 hasRelatedWork W2026036943 @default.
• W1699655904 hasRelatedWork W2044413922 @default.
• W1699655904 hasRelatedWork W2053392671 @default.
• W1699655904 hasRelatedWork W2072311401 @default.
• W1699655904 hasRelatedWork W2082560626 @default.
• W1699655904 hasRelatedWork W2091278332 @default.
• W1699655904 hasRelatedWork W2123100908 @default.
• W1699655904 hasRelatedWork W2128510017 @default.
• W1699655904 hasRelatedWork W2153575169 @default.

• next