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Is Valiant–Vazirani's isolation probability improvable?

2013
*
Computational Complexity
*

The

doi:10.1007/s00037-013-0059-7
fatcat:5f7ljbwnhvfatpomcvxpw6luym
*Valiant*-Vazirani procedure*is*randomized, and when C*is*satisfiable it produces a uniquely satisfiable circuit C with*probability*Ω(1/n). ...*Is*it possible to have an efficient deterministic witnessisolating procedure? Or, at least,*is*it possible to*improve*the success*probability*of a randomized procedure to a large constant? ... Another natural question*is*whether the success*probability*Ω(1/n) for randomized*isolation*can be*improved*to, say, a large constant*probability*. ...##
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Is Valiant-Vazirani's Isolation Probability Improvable?

2012
*
2012 IEEE 27th Conference on Computational Complexity
*

The

doi:10.1109/ccc.2012.22
dblp:conf/coco/DellKMW12
fatcat:kzanaystp5h4jmyvl6kyf2nklu
*Valiant*-Vazirani procedure*is*randomized, and when C*is*satisfiable it produces a uniquely satisfiable circuit C with*probability*Ω(1/n). ...*Is*it possible to have an efficient deterministic witnessisolating procedure? Or, at least,*is*it possible to*improve*the success*probability*of a randomized procedure to a large constant? ... Another natural question*is*whether the success*probability*Ω(1/n) for randomized*isolation*can be*improved*to, say, a large constant*probability*. ...##
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Boolean complexity classes vs. their arithmetic analogs

1996
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Random structures & algorithms (Print)
*

These reductions are based on the

doi:10.1002/(sici)1098-2418(199608/09)9:1/2<99::aid-rsa7>3.3.co;2-o
fatcat:vx7x7v7cj5dfvpj6m4d7cm3cr4
*Isolation*Lemma of Mulmuley, Vazirani and Vazirani. ... This paper provides logspace and small circuit depth analogs of the result of*Valiant*and Vazirani, which*is*a randomized (or nonuniform) reduction from N P to its arithmetic analog ⊕P . ... All our simulations (as well as*Valiant*-*Vazirani's*) are non-uniform (or at least randomized). ...##
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Boolean complexity classes vs. their arithmetic analogs

1996
*
Random structures & algorithms (Print)
*

These reductions are based on the

doi:10.1002/(sici)1098-2418(199608/09)9:1/2<99::aid-rsa7>3.0.co;2-6
fatcat:whcehawyzndv7hd6eyuurt2a7a
*Isolation*Lemma of Mulmuley, Vazirani and Vazirani. ... This paper provides logspace and small circuit depth analogs of the result of*Valiant*and Vazirani, which*is*a randomized (or nonuniform) reduction from N P to its arithmetic analog ⊕P . ... All our simulations (as well as*Valiant*-*Vazirani's*) are non-uniform (or at least randomized). ...##
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Shortest Two Disjoint Paths in Polynomial Time
[chapter]

2014
*
Lecture Notes in Computer Science
*

Our algorithm

doi:10.1007/978-3-662-43948-7_18
fatcat:ngjynw4pfbd23ey6xnkgvegb2e
*is*algebraic and uses permanents over the quotient ring Z4[X]/(X m ) in combination with Mulmuley, Vazirani and*Vazirani's**isolation*lemma to detect a solution. ... Given an undirected graph and two pairs of vertices (si, ti) for i ∈ {1, 2} we show that there*is*a polynomial time Monte Carlo algorithm that finds disjoint paths of smallest total length joining si and ... To work in full generality, our algorithm*is*randomized, using Mulmuley, Vazirani, and*Vazirani's**isolation*lemma [10] . Related problems. ...##
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NP might not be as easy as detecting unique solutions

1998
*
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
*

It

doi:10.1145/276698.276737
dblp:conf/stoc/BeigelBF98
fatcat:xjmozzrylbd5day56z4q3zfx7m
*is*the first such computable oracle. Relative to A we have a collapse of EXP A ZPP A P A /poly. ... We also create a different relativized world where there exists a set L in NP that*is*NP-complete under reductions that make one query to L but not complete under traditional many-one reductions. ...*Valiant*and*Vazirani's*construction creates random subspaces of the assignments. ...##
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A bibliographical study of grammatical inference

2005
*
Pattern Recognition
*

The goal of this paper

doi:10.1016/j.patcog.2005.01.003
fatcat:62qwskiqcvddjobakbdshwebqq
*is*to introduce a certain number of papers related with grammatical inference. ... There*is*no uniform literature on the subject and one can find many papers with original definitions or points of view. ...*is*published in Kearns and*Vazirani's*book [23] ). ...##
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Limits on Efficient Computation in the Physical World
[article]

2005
*
arXiv
*
pre-print

Could Bernstein and

arXiv:quant-ph/0412143v2
fatcat:x6mjz4h4gzaszbfgbkshgm2v3u
*Vazirani's*quantum algorithm for RFS be*improved*even further, to give an exponential speedup over the classical algorithm? ... However, Yao [248] showed that Bernstein and*Vazirani's*definition*is*equivalent to the much simpler one given here. ... Also, given a theory T , let P t and P ′ t be the joint*probabilities*matrices ...##
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Sparse Signal Processing with Frame Theory
[article]

2012
*
arXiv
*
pre-print

Many emerging applications involve sparse signals, and their processing

arXiv:1204.5958v1
fatcat:oga4af75uzflzmggxsye3idac4
*is*a subject of active research. ... Our use of random linear projections in the above reduction to Full Spark*is*similar in spirit to*Valiant*and*Vazirani's*use of random hash functions in their reduction to Unique SAT [138] . ... From here,*isolating*µ gives the claim. Lastly, for average coherence, pick some x ∈ F 2 m . ...