Filters








9 Hits in 1.9 sec

Is Valiant–Vazirani's isolation probability improvable?

Holger Dell, Valentine Kabanets, Dieter van Melkebeek, Osamu Watanabe
2013 Computational Complexity  
The 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.  ... 
doi:10.1007/s00037-013-0059-7 fatcat:5f7ljbwnhvfatpomcvxpw6luym

Is Valiant-Vazirani's Isolation Probability Improvable?

Holger Dell, Valentine Kabanets, Dieter van Melkebeek, Osamu Watanabe
2012 2012 IEEE 27th Conference on Computational Complexity  
The 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.  ... 
doi:10.1109/ccc.2012.22 dblp:conf/coco/DellKMW12 fatcat:kzanaystp5h4jmyvl6kyf2nklu

Boolean complexity classes vs. their arithmetic analogs

Anna Gál, Avi Wigderson
1996 Random structures & algorithms (Print)  
These reductions are based on the 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).  ... 
doi:10.1002/(sici)1098-2418(199608/09)9:1/2<99::aid-rsa7>3.3.co;2-o fatcat:vx7x7v7cj5dfvpj6m4d7cm3cr4

Boolean complexity classes vs. their arithmetic analogs

Anna G�l, Avi Wigderson
1996 Random structures & algorithms (Print)  
These reductions are based on the 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).  ... 
doi:10.1002/(sici)1098-2418(199608/09)9:1/2<99::aid-rsa7>3.0.co;2-6 fatcat:whcehawyzndv7hd6eyuurt2a7a

Shortest Two Disjoint Paths in Polynomial Time [chapter]

Andreas Björklund, Thore Husfeldt
2014 Lecture Notes in Computer Science  
Our algorithm 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.  ... 
doi:10.1007/978-3-662-43948-7_18 fatcat:ngjynw4pfbd23ey6xnkgvegb2e

NP might not be as easy as detecting unique solutions

Richard Beigel, Harry Buhrman, Lance Fortnow
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
It 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.  ... 
doi:10.1145/276698.276737 dblp:conf/stoc/BeigelBF98 fatcat:xjmozzrylbd5day56z4q3zfx7m

A bibliographical study of grammatical inference

Colin de la Higuera
2005 Pattern Recognition  
The goal of this paper 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] ).  ... 
doi:10.1016/j.patcog.2005.01.003 fatcat:62qwskiqcvddjobakbdshwebqq

Limits on Efficient Computation in the Physical World [article]

Scott Aaronson
2005 arXiv   pre-print
Could Bernstein and 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  ... 
arXiv:quant-ph/0412143v2 fatcat:x6mjz4h4gzaszbfgbkshgm2v3u

Sparse Signal Processing with Frame Theory [article]

Dustin G. Mixon
2012 arXiv   pre-print
Many emerging applications involve sparse signals, and their processing 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 .  ... 
arXiv:1204.5958v1 fatcat:oga4af75uzflzmggxsye3idac4