Filters








528 Hits in 3.4 sec

Randomness vs Time: Derandomization under a Uniform Assumption

Russell Impagliazzo, Avi Wigderson
2001 Journal of computer and system sciences (Print)  
First, is an average-case derandomization all one can hope for under a uniform assumption?  ...  . − SIZE Average-Case Derandomization under Uniform Assumptions Both the high-end and low-end results above require nonuniform hardness assumptions, i.e., that the hard problems in question are hard  ... 
doi:10.1006/jcss.2001.1780 fatcat:iqrss6b62vcrxmqd2mbii3oxcu

Randomness vs. Time in Anonymous Networks [chapter]

Jochen Seidel, Jara Uitto, Roger Wattenhofer
2015 Lecture Notes in Computer Science  
We establish that for any reasonable target function f , there is a randomized 2-hop coloring scheme running in O(f (n)) time.  ...  Since any randomized anonymous network algorithm can be decomposed into a randomized 2-hop coloring stage and a deterministic stage, we tackle the question by focusing on the randomized stage.  ...  Under the assumption of uniform algorithms, the leader election impossibility result from [3] extends to the case where randomization is available.  ... 
doi:10.1007/978-3-662-48653-5_18 fatcat:i2tvb55hhvhb7fs6tu7plh42wy

Stoquastic PCP vs. Randomness [article]

Dorit Aharonov, Alex B. Grilo
2019 arXiv   pre-print
The derandomization of MA, the probabilistic version of NP, is a long standing open question. In this work, we connect this problem to a variant of another major problem: the quantum PCP conjecture.  ...  They proved the MA-completeness of the problem of deciding whether the groundenergy of a uniform stoquastic local Hamiltonian is zero or inverse polynomial.  ...  in randomized polynomial time.  ... 
arXiv:1901.05270v2 fatcat:qcryivy4sjcgpe6w5j4gxjngta

Derandomization under uniform assumptions [article]

Antonios A. Antonopoulos, National Technological University Of Athens, National Technological University Of Athens, Ευστάθιος Ζάχος
2014
Recent advances have proven that it is possible, under some reasonable assumptions, to replace a BPP randomized algorithm with a deterministic one (i.e., to derandomize), only with polynomial loss of efficiency  ...  he Uniform Distribution).  ...  Chapter 6 Uniform Derandomization of RP Valentine Kabanets obtained in [Kab00] another derandomizing result, for RP this time, under the -weaker-assumption that EXP � = ZPP.  ... 
doi:10.26240/heal.ntua.5868 fatcat:7xvr5nb7ybalddsvmaiqs7t7ee

Low-end uniform hardness vs. randomness tradeoffs for AM

Ronen Shaltiel, Christopher Umans
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
In this work, we give uniform hardness vs. randomness tradeoffs for AM that are near-optimal for the full range of possible hardness assumptions.  ...  In 2003, Gutfreund, Shaltiel and Ta-Shma [GSTS03] proved a uniform hardness vs. randomness tradeoff for AM, but that result only worked on the "high-end" of possible hardness assumptions.  ...  Uniform hardness versus randomness tradeoffs for AM A non-black-box uniform reduction for derandomizing AM in the high-end was given in [GSTS03] . It yields gap theorems for both AM and AM ∩ coAM.  ... 
doi:10.1145/1250790.1250854 dblp:conf/stoc/ShaltielU07 fatcat:rubsqhu67najncnqaetyywxj44

Partition testing vs. random testing: the influence of uncertainty

W.J. Gutjahr
1999 IEEE Transactions on Software Engineering  
testing can be up to k times higher than that of random testing, where k is the number of subdomains.  ...  This paper compares partition testing and random testing on the assumption that program failure rates are not known with certainty before testing and are, therefore, modeled by random variables.  ...  Bomze, A. Futschik, and E.J. Weyuker for valuable hints and comments. Furthermore, the author is indebted to the anonymous referees for their profound and helpful remarks on the first versions.  ... 
doi:10.1109/32.815325 fatcat:533bzwa3v5g7fcekvjkuzo3pma

Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading [article]

Zeyu Guo, He Sun
2013 arXiv   pre-print
Second, we show a reduction from rumor spreading processes to branching programs, and this reduction provides a general framework to derandomize gossip processes.  ...  First, we establish a connection between rumor spreading processes and Markov chains, which is used to approximate the rumor spreading time by the mixing time of Markov chains.  ...  The cases for Y S u,v and Y S u,v Y S w,x are the same, except that the time is reversed. Now we are ready to prove a derandomized version of Lemma D.16. Theorem D. 19 .  ... 
arXiv:1311.2839v1 fatcat:f3cnyulvzjcqzpt2ttudpjgmku

Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading [chapter]

Zeyu Guo, He Sun
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
Second, we show a reduction from rumor spreading processes to branching programs, and this reduction provides a general framework to derandomize gossip processes.  ...  First, we establish a connection between rumor spreading processes and Markov chains, which is used to approximate the rumor spreading time by the mixing time of Markov chains.  ...  The cases for Y S u,v and Y S u,v Y S w,x are the same, except that the time is reversed. Now we are ready to prove a derandomized version of Lemma D.16. Theorem D. 19 .  ... 
doi:10.1137/1.9781611973730.29 dblp:conf/soda/Guo015 fatcat:kkci55pwundg5m3h5a3ctcnp24

In search of an easy witness: exponential time vs. probabilistic polynomial time

Russell Impagliazzo, Valentine Kabanets, Avi Wigderson
2002 Journal of computer and system sciences (Print)  
Restricting the search space f0; 1g n to the set of truth tables of "easy" Boolean functions on log n variables, as well as using some known hardness-randomness tradeoffs, we establish a number of results  ...  In particular, we show that NEXPCP=poly3NEXP ¼ MA; this can be interpreted as saying that no derandomization of MA (and, hence, of promise-BPP) is possible unless NEXP contains a hard Boolean function.  ...  EXP ¼ BPP3EE ¼ BPE: Our proof will rely on the following result by Impagliazzo and Wigderson [IW98] on the derandomization of BPP under a uniform hardness assumption.  ... 
doi:10.1016/s0022-0000(02)00024-7 fatcat:lvshl4tmdrbnlaqly4ejcoarri

On Derandomizing Probabilistic Sublinear-Time Algorithms

Marius Zimand
2007 Proceedings - IEEE Conference on Computational Complexity  
There exists a positive constant α < 1 such that for any function T (n) ≤ n α and for any problem L ∈ BPTIME(T (n)), there exists a deterministic algorithm running in poly(T (n)) time which decides L,  ...  except for at most a 2 −Ω(T (n) log T (n)) fraction of inputs of length n.  ...  Impagliazzo and A. Wigderson. Random- ness vs. time: De-randomization under a uni- form assumption.  ... 
doi:10.1109/ccc.2007.19 dblp:conf/coco/Zimand07 fatcat:ar7csockojgwhdh2rwekem3pca

Randomness vs. time: de-randomization under a uniform assumption

R. Impagliazzo, A. Wigderson
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)  
This is the first derandomization result for BP P based on uniform, noncryptographic hardness assumptions.  ...  They give a non-constructive argument that a circuit distinguishing the pseudo-random strings from truly random strings implies that a similarly-sized circuit exists computing the "hard function".  ...  First, is an average-case derandomization all one can hope for under a uniform assumption?  ... 
doi:10.1109/sfcs.1998.743524 dblp:conf/focs/ImpagliazzoW98 fatcat:toh4bsfmgbcyffkogvz3lpa5t4

Derandomizing Arthur-Merlin Games under Uniform Assumptions [chapter]

Chi-Jen Lu
2000 Lecture Notes in Computer Science  
In particular, we show two ways of derandomizing the complexity class AM under uniform assumptions, which was only known previously under nonuniform assumptions.  ...  Similar tradeoffs also hold for a whole range of parameters.  ...  Our first result is inspired by that of Kabanets (2000) on derandomizing RP under some uniform assumption.  ... 
doi:10.1007/3-540-40996-3_26 fatcat:3r7bguaabbaulbhe6ergxkdnt4

Derandomizing Arthur--Merlin games under uniform assumptions

C.-J. Lu
2001 Computational Complexity  
In particular, we show two ways of derandomizing the complexity class AM under uniform assumptions, which was only known previously under nonuniform assumptions.  ...  Similar tradeoffs also hold for a whole range of parameters.  ...  Our first result is inspired by that of Kabanets (2000) on derandomizing RP under some uniform assumption.  ... 
doi:10.1007/s00037-001-8196-9 fatcat:xa7tuxxpxjfhldmbbrk3hils34

Pseudo-Derandomizing Learning and Approximation

Igor Carboni Oliveira, Rahul Santhanam, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
In the setting of learning with membership queries, we first show that randomized learning algorithms can be derandomized (resp. pseudo-derandomized) under the standard hardness assumption that E (resp  ...  Our goal is to simulate known randomized algorithms in these settings by pseudo-deterministic algorithms in a generic fashion -a goal we succinctly term pseudo-derandomization. Learning.  ...  The result is then a direct consequence of Lemma 6 and the hardness vs. randomness paradigm (Theorem 17).  ... 
doi:10.4230/lipics.approx-random.2018.55 dblp:conf/approx/OliveiraS18 fatcat:gjphuxvvubakxevkekyacqxryq

Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

Dan Gutfreund, Ronen Shaltiel, Amnon Ta-Shma
2003 Computational Complexity  
Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap theorem" for BPP.  ...  that derandomize BPP, MA and AM using "necessary assumptions" (i.e., assumptions that are implied by the existence of pseudo-random generators).  ...  Explicit Constructions Under Uniform Assumptions Klivans and Van-Melkebeek [KvM99] suggested a general framework for derandomization under hardness assumptions.  ... 
doi:10.1007/s00037-003-0178-7 fatcat:zea4gq5hpjaqnlldauryyjdeqe
« Previous Showing results 1 — 15 out of 528 results