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Randomness vs Time: Derandomization under a Uniform Assumption

2001
*
Journal of computer and system sciences (Print)
*

First, is an average-case

doi:10.1006/jcss.2001.1780
fatcat:iqrss6b62vcrxmqd2mbii3oxcu
*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 ...##
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Randomness vs. Time in Anonymous Networks
[chapter]

2015
*
Lecture Notes in Computer Science
*

We establish that for any reasonable target function f , there is

doi:10.1007/978-3-662-48653-5_18
fatcat:i2tvb55hhvhb7fs6tu7plh42wy
*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. ...##
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Stoquastic PCP vs. Randomness
[article]

2019
*
arXiv
*
pre-print

The

arXiv:1901.05270v2
fatcat:qcryivy4sjcgpe6w5j4gxjngta
*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*. ...##
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Derandomization under uniform assumptions
[article]

2014

Recent advances have proven that it is possible,

doi:10.26240/heal.ntua.5868
fatcat:7xvr5nb7ybalddsvmaiqs7t7ee
*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. ...##
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Low-end uniform hardness vs. randomness tradeoffs for AM

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

In this work, we give

doi:10.1145/1250790.1250854
dblp:conf/stoc/ShaltielU07
fatcat:rubsqhu67najncnqaetyywxj44
*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. ...##
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Partition testing vs. random testing: the influence of uncertainty

1999
*
IEEE Transactions on Software Engineering
*

testing can be up to k

doi:10.1109/32.815325
fatcat:533bzwa3v5g7fcekvjkuzo3pma
*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. ...##
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Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading
[article]

2013
*
arXiv
*
pre-print

Second, we show

arXiv:1311.2839v1
fatcat:f3cnyulvzjcqzpt2ttudpjgmku
*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 . ...##
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Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading
[chapter]

2014
*
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Second, we show

doi:10.1137/1.9781611973730.29
dblp:conf/soda/Guo015
fatcat:kkci55pwundg5m3h5a3ctcnp24
*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 . ...##
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In search of an easy witness: exponential time vs. probabilistic polynomial time

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-

doi:10.1016/s0022-0000(02)00024-7
fatcat:lvshl4tmdrbnlaqly4ejcoarri
*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*. ...##
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On Derandomizing Probabilistic Sublinear-Time Algorithms

2007
*
Proceedings - IEEE Conference on Computational Complexity
*

There exists

doi:10.1109/ccc.2007.19
dblp:conf/coco/Zimand07
fatcat:ar7csockojgwhdh2rwekem3pca
*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*. ...##
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Randomness vs. time: de-randomization under a uniform assumption

*
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
*

This is the first

doi:10.1109/sfcs.1998.743524
dblp:conf/focs/ImpagliazzoW98
fatcat:toh4bsfmgbcyffkogvz3lpa5t4
*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*? ...##
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Derandomizing Arthur-Merlin Games under Uniform Assumptions
[chapter]

2000
*
Lecture Notes in Computer Science
*

In particular, we show two ways of

doi:10.1007/3-540-40996-3_26
fatcat:3r7bguaabbaulbhe6ergxkdnt4
*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*. ...##
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Derandomizing Arthur--Merlin games under uniform assumptions

2001
*
Computational Complexity
*

In particular, we show two ways of

doi:10.1007/s00037-001-8196-9
fatcat:xa7tuxxpxjfhldmbbrk3hils34
*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*. ...##
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Pseudo-Derandomizing Learning and Approximation

2018
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

In the setting of learning with membership queries, we first show that

doi:10.4230/lipics.approx-random.2018.55
dblp:conf/approx/OliveiraS18
fatcat:gjphuxvvubakxevkekyacqxryq
*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). ...##
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Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

2003
*
Computational Complexity
*

Impagliazzo and Wigderson proved

doi:10.1007/s00037-003-0178-7
fatcat:zea4gq5hpjaqnlldauryyjdeqe
*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*. ...
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