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On Efficient Zero-Knowledge PCPs [chapter]

Yuval Ishai, Mohammad Mahmoody, Amit Sahai
2012 Lecture Notes in Computer Science  
Black-Box Sublinear ZK Arguments via ZK-PCPs.  ...  Assuming that the polynomial time hierarchy does not collapse, we settle the above question in the negative for ZK-PCPs in which the verifier is nonadaptive (i.e. the queries only depend on the input and  ...  hierarchy collapses.  ... 
doi:10.1007/978-3-642-28914-9_9 fatcat:by5mj3efbnb6xdqvdkvcgtp5qa

On Medium-Uniformity and Circuit Lower Bounds

Rahul Santhanam, Ryan Williams
2013 2013 IEEE Conference on Computational Complexity  
Lower Bounds Against Medium-Uniform Circuits.  ...  We complement these results by showing how to convert any potential simulation of LOGTIME-uniform NC 1 in ACC 0 /poly or TC 0 /poly into a medium-uniform simulation using small advice.  ...  LOWER BOUNDS AGAINST MEDIUM UNIFORMITY We will use a folklore result about a time hierarchy for deterministic time, where the lower bound holds against sublinear advice.  ... 
doi:10.1109/ccc.2013.40 dblp:conf/coco/SanthanamW13 fatcat:mm4ls445rjd37mkuqv5sg2lqiy

On Uniformity and Circuit Lower Bounds

Rahul Santhanam, Ryan Williams
2014 Computational Complexity  
Applying the hypothesis multiple times allows us to simulate medium-uniformity with a very small amount of nonuniform advice and diagonalize against the small-advice simulation to derive a contradiction  ...  Lower bounds against medium-uniform circuits.  ...  Lower bounds against medium uniformity We will use a folklore result about a time hierarchy for deterministic time, where the lower bound holds against sublinear advice. Proposition 2.1.  ... 
doi:10.1007/s00037-014-0087-y fatcat:4fy5xs7jrfbtzm37apd7wq2qza

Lower Bounds Against Weakly-Uniform Threshold Circuits

Ruiwen Chen, Valentine Kabanets, Jeff Kinne
2013 Algorithmica  
A family of Boolean circuits {Cn} n 0 is called γ(n)-weakly-uniform if there is a polynomialtime algorithm for deciding the direct-connection language of every Cn, given advice of size γ(n).  ...  weaker circuit class, as polynomial-size constant-depth arith-4 A plausible explanation of this "barrier" is given by the "natural proofs" framework of [RR97], who argue it is hard to prove lower bounds against  ...  One result is a diagonalization argument against alternating Turing machines with advice, getting a language in the counting hierarchy CH that is "hard" against weakly-uniform TC 0 circuits of certain  ... 
doi:10.1007/s00453-013-9823-y fatcat:qhysc73akvgzjgzdxl5d5ymula

Optimal advice

Lane A. Hemaspaandra, Leen Torenvliet
1996 Theoretical Computer Science  
We show linear advice to be optimal. * Corresponding autbor.  ...  Ko proved that the P-selective sets are in the advice class P/quadratic, and Hemaspaandra, Naik, Ogihara, and Selman showed that they are in PPilinear.  ...  Selman for pointing out that P = PP =+ P-sel C P/linear, and P. van Emde Boas for pointing out the intermediate Points in the advice-nondeterminism n-ade-off.  ... 
doi:10.1016/0304-3975(95)00076-3 fatcat:irjeovuzfnfwxf3bq77gufw5am

A Survey of Lower Bounds for Satisfiability and Related Problems

Dieter van Melkebeek
2006 Foundations and Trends® in Theoretical Computer Science  
If our hypothetical machines solving hard problems have advice, we can pass along and collect all the advice strings we need during the various transformations.  ...  For future use, we parameterize the lemma with the efficiency of the speedup of deterministic sublinear-space computations in the second level of the polynomial-time hierarchy.  ... 
doi:10.1561/0400000012 fatcat:vsdohimqr5a5zlbat3l37uwdem

Computational Complexity of Space-Bounded Real Numbers [article]

Masaki Nakanishi, Marcos Villagra
2018 arXiv   pre-print
First, N must compares its input d against the output γ of M φx using space O(s(n)). To compare d against γ using space O(s(n)) it suffices to remember only one symbol of γ at a time.  ...  A deterministic finite automaton with advice has a read-only advice tape in which an advice string is written prior to the computation.  ...  Let l adv be the length of an advice string and let Q be the set of states of the automaton.  ... 
arXiv:1805.02572v1 fatcat:orwjbefxu5hm5lx3latsj4or2e

Incomputability at the foundations of physics (A study in the philosophy of science)

J. F. Costa
2013 Journal of Logic and Computation  
Proposition 5.6 (Recursive β) If β is PRED β π -identifiable for some strictly sublinear π, having β as advice, then β is total computable. Proof.  ...  The hierarchy of predictive scientists reflects the hierarchy of timescales.  ... 
doi:10.1093/logcom/ext048 fatcat:qff7oxt545cm5jzjt2e4pplpym

Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds

Jeff Kinne, Dieter van Melkebeek, Ronen Shaltiel
2011 Computational Complexity  
Zimand [Zim08] showed unconditional typically-correct derandomizations with polynomial overhead for sublinear-time algorithms, which can be viewed as randomized decision trees that use a sublinear number  ...  The bit length of the advice is bounded by the logarithm of (8).  ...  In particular, if H has the stated hardness against circuits that have oracle gates for an oracle O, then NW H;n,m is ǫ-pseudorandom for tests T with the stated parameters that have access to O oracle  ... 
doi:10.1007/s00037-011-0019-z fatcat:6w32whkz7bahfkrxjko2klxgli

Self-reducibility

JoséL. Balcázar
1990 Journal of computer and system sciences (Print)  
Moreover, the round robin technique (playing all advices against each other) is not used in the proofs.  ...  those defined by polynomially long advice.  ... 
doi:10.1016/0022-0000(90)90025-g fatcat:6xxf36pjyfh4hhdyuqahyq4f3q

On the Feasibility of Consistent Computations [chapter]

Sven Laur, Helger Lipmaa
2010 Lecture Notes in Computer Science  
Given advice a k , A k outputs certificates (s 1 , . . . , s m ) ← A k (a k ). 5.  ...  A natural alternative is to use a sublinear-length commitment scheme together with suitable zero-knowledge techniques as detailed in [24] .  ... 
doi:10.1007/978-3-642-13013-7_6 fatcat:342ngsug6ndengm7hcqamuywx4

A sublinear algorithm for approximate keyword searching

E. W. Myers
1994 Algorithmica  
Apart from the fact that our algorithm is "truly" sublinear, it also has the advantage over the Chang and Lawler algorithm that the degree of sublinearity just depends on ε and not on P.  ...  They term their algorithm sublinear in the sense of Boyer and Moore [BoM77], i.e., cN characters of A are examined where c < 1.  ...  Acknowledgement The author wishes to thank his colleague and mentor Andrzej Ehrenfeucht for his advice, ideas, and encouragement early in the development of this work.  ... 
doi:10.1007/bf01185432 fatcat:mggn2aq5a5dhlcdcy4gwcjc3au

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)  
In Section 5.1, we show that (for nondeterministic Turing machines with sublinear amount of advice) if the problem of circuit approximation can be solved efficiently at all, then it can also be solved  ...  That is, does the existence of a P-natural property useful against P=poly imply that EXPgP=poly?  ... 
doi:10.1016/s0022-0000(02)00024-7 fatcat:lvshl4tmdrbnlaqly4ejcoarri

Deterministic MDPs with Adversarial Rewards and Bandit Feedback [article]

Raman Arora, Ofer Dekel, Ambuj Tewari
2012 arXiv   pre-print
Under mild assumptions on the structure of the transition dynamics, we prove that MarcoPolo enjoys a regret of O(T^(3/4)sqrt(log(T))) against the best deterministic policy in hindsight.  ...  Arora et al. (2012) also presents a general reduction that converts any bandit algorithm with a sublinear regret into an algorithm with a sublinear policy regret.  ...  de Farias and Megiddo (2006) propose algorithms that combine expert advice in a reactive environment.  ... 
arXiv:1210.4843v1 fatcat:fyxownfssjbtdh76d7wcoty6lm

Lower Bounds for Swapping Arthur and Merlin [chapter]

Scott Diehl
2007 Lecture Notes in Computer Science  
This improves recent results that give such lower bounds for problems in the second level of the polynomial-time hierarchy. * This paper is the full version of an extended abstract to appear at RANDOM  ...  Acknowledgments The author would like to thank Bess Berg, Jeff Kinne, and Emanuele Viola for their helpful discussions, and especially Dieter van Melkebeek for his extensive advice, support, and enthusiasm  ...  such a collapse with sublinear factor increase in time per alternation, which could yield new time-space lower bounds for counting problems.  ... 
doi:10.1007/978-3-540-74208-1_33 fatcat:rpew5cdjyrbs7dqvrmzbvwsjda
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