FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1497568429> ?p ?o ?g. }

• W1497568429 abstract "Sipser and GAƒÂics, and independently Lautemann, proved in '83 that probabilistic polynomial time is contained in the second level of the polynomial-time hierarchy, i.e. BPP is in Sigma_2 P. This is essentially the only non-trivial upper bound that we have on the power of probabilistic computation. More precisely, the Sipser-GAƒÂics-Lautemann simulation shows that probabilistic time can be simulated deterministically, using two quantifiers, **with a quadratic blow-up in the running time**. That is, BPTime(t) is contained in Sigma_2 Time(t^2).In this talk we discuss whether this quadratic blow-up in the running time is necessary. We show that the quadratic blow-up is indeed necessary for black-box simulations that use two quantifiers, such as those of Sipser, GAƒÂics, and Lautemann. To obtain this result, we prove a new circuit lower bound for computing **approximate majority**, i.e. computing the majority of a given bit-string whose fraction of 1's is bounded away from 1/2 (by a constant): We show that small depth-3 circuits for approximate majority must have bottom fan-in Omega(log n).On the positive side, we obtain that probabilistic time can be simulated deterministically, using three quantifiers, in quasilinear time. That is, BPTime(t) is contained in Sigma_3 Time(t polylog t). Along the way, we show that approximate majority can be computed by uniform polynomial-size depth-3 circuits. This is a uniform version of a striking result by Ajtai that gives *non-uniform* polynomial-size depth-3 circuits for approximate majority.If time permits, we will discuss some applications of our results to proving lower bounds on randomized Turing machines." @default.
• W1497568429 created "2016-06-24" @default.
• W1497568429 creator A5072846764 @default.
• W1497568429 date "2005-01-01" @default.
• W1497568429 modified "2023-09-23" @default.
• W1497568429 title "On Probabilistic Time versus Alternating Time" @default.
• W1497568429 cites W1975124543 @default.
• W1497568429 cites W1981030589 @default.
• W1497568429 cites W2007671490 @default.
• W1497568429 cites W2010699490 @default.
• W1497568429 cites W2011438986 @default.
• W1497568429 cites W2014603110 @default.
• W1497568429 cites W2017609259 @default.
• W1497568429 cites W2036095420 @default.
• W1497568429 cites W2043280328 @default.
• W1497568429 cites W2047342855 @default.
• W1497568429 cites W2048958388 @default.
• W1497568429 cites W2060270693 @default.
• W1497568429 cites W2067378208 @default.
• W1497568429 cites W2075449032 @default.
• W1497568429 cites W2079192595 @default.
• W1497568429 cites W2109520329 @default.
• W1497568429 cites W2111642906 @default.
• W1497568429 cites W2131798840 @default.
• W1497568429 cites W2137423523 @default.
• W1497568429 cites W2139964991 @default.
• W1497568429 cites W2163137752 @default.
• W1497568429 cites W2340787257 @default.
• W1497568429 cites W2480498821 @default.
• W1497568429 cites W2610637368 @default.
• W1497568429 cites W2611754984 @default.
• W1497568429 cites W3018694765 @default.
• W1497568429 cites W3145128584 @default.
• W1497568429 cites W66508742 @default.
• W1497568429 hasPublicationYear "2005" @default.
• W1497568429 type Work @default.
• W1497568429 sameAs 1497568429 @default.
• W1497568429 citedByCount "0" @default.
• W1497568429 crossrefType "journal-article" @default.
• W1497568429 hasAuthorship W1497568429A5072846764 @default.
• W1497568429 hasConcept C105795698 @default.
• W1497568429 hasConcept C11413529 @default.
• W1497568429 hasConcept C114614502 @default.
• W1497568429 hasConcept C118615104 @default.
• W1497568429 hasConcept C121332964 @default.
• W1497568429 hasConcept C129844170 @default.
• W1497568429 hasConcept C134306372 @default.
• W1497568429 hasConcept C162324750 @default.
• W1497568429 hasConcept C199360897 @default.
• W1497568429 hasConcept C2524010 @default.
• W1497568429 hasConcept C2777027219 @default.
• W1497568429 hasConcept C2778049214 @default.
• W1497568429 hasConcept C3017489831 @default.
• W1497568429 hasConcept C311688 @default.
• W1497568429 hasConcept C31170391 @default.
• W1497568429 hasConcept C33923547 @default.
• W1497568429 hasConcept C34388435 @default.
• W1497568429 hasConcept C34447519 @default.
• W1497568429 hasConcept C41008148 @default.
• W1497568429 hasConcept C49937458 @default.
• W1497568429 hasConcept C62520636 @default.
• W1497568429 hasConcept C77553402 @default.
• W1497568429 hasConcept C90119067 @default.
• W1497568429 hasConceptScore W1497568429C105795698 @default.
• W1497568429 hasConceptScore W1497568429C11413529 @default.
• W1497568429 hasConceptScore W1497568429C114614502 @default.
• W1497568429 hasConceptScore W1497568429C118615104 @default.
• W1497568429 hasConceptScore W1497568429C121332964 @default.
• W1497568429 hasConceptScore W1497568429C129844170 @default.
• W1497568429 hasConceptScore W1497568429C134306372 @default.
• W1497568429 hasConceptScore W1497568429C162324750 @default.
• W1497568429 hasConceptScore W1497568429C199360897 @default.
• W1497568429 hasConceptScore W1497568429C2524010 @default.
• W1497568429 hasConceptScore W1497568429C2777027219 @default.
• W1497568429 hasConceptScore W1497568429C2778049214 @default.
• W1497568429 hasConceptScore W1497568429C3017489831 @default.
• W1497568429 hasConceptScore W1497568429C311688 @default.
• W1497568429 hasConceptScore W1497568429C31170391 @default.
• W1497568429 hasConceptScore W1497568429C33923547 @default.
• W1497568429 hasConceptScore W1497568429C34388435 @default.
• W1497568429 hasConceptScore W1497568429C34447519 @default.
• W1497568429 hasConceptScore W1497568429C41008148 @default.
• W1497568429 hasConceptScore W1497568429C49937458 @default.
• W1497568429 hasConceptScore W1497568429C62520636 @default.
• W1497568429 hasConceptScore W1497568429C77553402 @default.
• W1497568429 hasConceptScore W1497568429C90119067 @default.
• W1497568429 hasOpenAccess W1497568429 @default.
• W1497568429 hasRelatedWork W1538026599 @default.
• W1497568429 hasRelatedWork W1615793053 @default.
• W1497568429 hasRelatedWork W2113448924 @default.
• W1497568429 hasRelatedWork W2157709541 @default.
• W1497568429 hasRelatedWork W2281668463 @default.
• W1497568429 hasRelatedWork W2397943364 @default.
• W1497568429 hasRelatedWork W2462702417 @default.
• W1497568429 hasRelatedWork W2465024128 @default.
• W1497568429 hasRelatedWork W2555351142 @default.
• W1497568429 hasRelatedWork W2593125389 @default.
• W1497568429 hasRelatedWork W2751668514 @default.
• W1497568429 hasRelatedWork W275231650 @default.
• W1497568429 hasRelatedWork W2790350908 @default.

• next