Matches in SemOpenAlex for { <https://semopenalex.org/work/W2511762567> ?p ?o ?g. }
Showing items 1 to 95 of
95
with 100 items per page.
- W2511762567 endingPage "1447" @default.
- W2511762567 startingPage "1433" @default.
- W2511762567 abstract "We present a deterministic $2^{O(t)}q^{frac{t-2}{t-1}+o(1)}$ algorithm to decide whether a univariate polynomial $f$, with $t$ monomial terms and degree $<q$, has a root in the finite field $mathbb{F}_q$. Our method is the first with complexity sublinear in $q$ when $t$ is fixed. We also prove a structural property for the nonzero roots in $mathbb{F}_q$ of any $t$-nomial: The nonzero roots always admit a partition into no more than $2(q-1)^{frac{t-2}{t-1}}$ cosets, each associated with one of two subgroups $S_1subseteq S_2$ of $mathbb{F}^*_q$. This can be thought of as a finite field analogue of Descartes' rule. A corollary of our results is the first deterministic sublinear algorithm for detecting common degree-one factors of $k$-tuples of $t$-nomials in $mathbb{F}_q[x]$ when $k$ and $t$ are fixed. When $t$ is not fixed we show that, for $p$ prime, detecting roots in $mathbb{F}_p$ for $f$ is $mathbf{NP}$-hard with respect to $mathbf{BPP}$-reductions. Finally, we prove that if the complexity of root detection is sublinear (in a refined sense), relative to the straight-line program encoding, then $mathbf{NEXP}nsubseteqmathbf{P/poly}$." @default.
- W2511762567 created "2016-09-16" @default.
- W2511762567 creator A5005847878 @default.
- W2511762567 creator A5008004564 @default.
- W2511762567 creator A5035238307 @default.
- W2511762567 date "2016-01-01" @default.
- W2511762567 modified "2023-09-26" @default.
- W2511762567 title "Sublinear Root Detection and New Hardness Results for Sparse Polynomials over Finite Fields" @default.
- W2511762567 cites W191763761 @default.
- W2511762567 cites W1973452640 @default.
- W2511762567 cites W1979366382 @default.
- W2511762567 cites W1980469175 @default.
- W2511762567 cites W1985572324 @default.
- W2511762567 cites W1998322533 @default.
- W2511762567 cites W2009505312 @default.
- W2511762567 cites W2031046967 @default.
- W2511762567 cites W2034013822 @default.
- W2511762567 cites W2035816523 @default.
- W2511762567 cites W2052965490 @default.
- W2511762567 cites W2072221429 @default.
- W2511762567 cites W2080132708 @default.
- W2511762567 cites W2095017199 @default.
- W2511762567 cites W2108397696 @default.
- W2511762567 cites W2108888104 @default.
- W2511762567 cites W2141040012 @default.
- W2511762567 cites W2158747250 @default.
- W2511762567 cites W2170368342 @default.
- W2511762567 cites W2207819601 @default.
- W2511762567 cites W2325723526 @default.
- W2511762567 cites W2963445336 @default.
- W2511762567 doi "https://doi.org/10.1137/140990401" @default.
- W2511762567 hasPublicationYear "2016" @default.
- W2511762567 type Work @default.
- W2511762567 sameAs 2511762567 @default.
- W2511762567 citedByCount "4" @default.
- W2511762567 countsByYear W25117625672015 @default.
- W2511762567 countsByYear W25117625672017 @default.
- W2511762567 countsByYear W25117625672019 @default.
- W2511762567 countsByYear W25117625672022 @default.
- W2511762567 crossrefType "journal-article" @default.
- W2511762567 hasAuthorship W2511762567A5005847878 @default.
- W2511762567 hasAuthorship W2511762567A5008004564 @default.
- W2511762567 hasAuthorship W2511762567A5035238307 @default.
- W2511762567 hasBestOaLocation W25117625672 @default.
- W2511762567 hasConcept C11252640 @default.
- W2511762567 hasConcept C114614502 @default.
- W2511762567 hasConcept C117160843 @default.
- W2511762567 hasConcept C118615104 @default.
- W2511762567 hasConcept C121332964 @default.
- W2511762567 hasConcept C134306372 @default.
- W2511762567 hasConcept C24890656 @default.
- W2511762567 hasConcept C2775997480 @default.
- W2511762567 hasConcept C33923547 @default.
- W2511762567 hasConcept C42812 @default.
- W2511762567 hasConcept C77926391 @default.
- W2511762567 hasConcept C85307737 @default.
- W2511762567 hasConcept C90119067 @default.
- W2511762567 hasConceptScore W2511762567C11252640 @default.
- W2511762567 hasConceptScore W2511762567C114614502 @default.
- W2511762567 hasConceptScore W2511762567C117160843 @default.
- W2511762567 hasConceptScore W2511762567C118615104 @default.
- W2511762567 hasConceptScore W2511762567C121332964 @default.
- W2511762567 hasConceptScore W2511762567C134306372 @default.
- W2511762567 hasConceptScore W2511762567C24890656 @default.
- W2511762567 hasConceptScore W2511762567C2775997480 @default.
- W2511762567 hasConceptScore W2511762567C33923547 @default.
- W2511762567 hasConceptScore W2511762567C42812 @default.
- W2511762567 hasConceptScore W2511762567C77926391 @default.
- W2511762567 hasConceptScore W2511762567C85307737 @default.
- W2511762567 hasConceptScore W2511762567C90119067 @default.
- W2511762567 hasFunder F4320337387 @default.
- W2511762567 hasIssue "4" @default.
- W2511762567 hasLocation W25117625671 @default.
- W2511762567 hasLocation W25117625672 @default.
- W2511762567 hasLocation W25117625673 @default.
- W2511762567 hasLocation W25117625674 @default.
- W2511762567 hasOpenAccess W2511762567 @default.
- W2511762567 hasPrimaryLocation W25117625671 @default.
- W2511762567 hasRelatedWork W1511142191 @default.
- W2511762567 hasRelatedWork W1764529246 @default.
- W2511762567 hasRelatedWork W2142266808 @default.
- W2511762567 hasRelatedWork W2265965672 @default.
- W2511762567 hasRelatedWork W2403541957 @default.
- W2511762567 hasRelatedWork W2949297756 @default.
- W2511762567 hasRelatedWork W2970640972 @default.
- W2511762567 hasRelatedWork W3089295049 @default.
- W2511762567 hasRelatedWork W3164555804 @default.
- W2511762567 hasRelatedWork W4292770613 @default.
- W2511762567 hasVolume "45" @default.
- W2511762567 isParatext "false" @default.
- W2511762567 isRetracted "false" @default.
- W2511762567 magId "2511762567" @default.
- W2511762567 workType "article" @default.