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Oblivious bounds on the probability of boolean functions

2014
*
ACM Transactions on Database Systems
*

This paper develops upper and lower

doi:10.1145/2532641
fatcat:6lehdkydyndzflh7rkerohgelq
*bounds*for*the**probability**of**Boolean**functions*by treating multiple occurrences*of*variables as independent and assigning them new individual*probabilities*. ... We call this approach dissociation and give an exact characterization*of*optimal*oblivious**bounds*, i.e. when*the*new*probabilities*are chosen independent*of**the**probabilities**of*all other variables. ... More information about this research, including*the*PostgreSQL statements to repeat*the*experiments*on*TPC-H data, can be found*on**the*project page: http://LaPushDB.com/. ...##
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Making Branching Programs Oblivious Requires Superlogarithmic Overhead

2011
*
2011 IEEE 26th Annual Conference on Computational Complexity
*

These are also

doi:10.1109/ccc.2011.35
dblp:conf/coco/BeameM11
fatcat:llp2k6z6g5gwxhql6d3vwgz5qa
*the*first lower*bounds*for randomized*oblivious*branching programs computing explicit*functions*that apply for T = ω(n log n). ... We give a similar time-space tradeoff*of*T = Ω'n log( n S ) log log( n S )´for*Boolean*randomized*oblivious*branching programs computing GIP -M AP , a variation*of**the*generalized inner product problem ... for separations for*Boolean*branching programs based*on*pseudorandom permutations*of**the*generalized inner product. ...##
###
Meanders and their applications in lower bounds arguments

1988
*
Journal of computer and system sciences (Print)
*

In particular, an Q (n log n) lower

doi:10.1016/0022-0000(88)90002-5
fatcat:c5gyqtmzurcctnugwnrql2n5ja
*bound**on**the*length*of*any such program for*the*majority*function**of*n bits is proved. ... We then apply these*bounds*to improve existing lower*bounds**on**the*length*of*constant width branching programs for various symmetric*functions*. ... input*oblivious*) branching programs*of*width w for these*functions*. ( [2] gives an additional lower*bound**on**the*size, but only a matching (and for some values*of*w slightly weaker) lower*bound**on**the*...##
###
Lower bounds for deterministic and nondeterministic branching programs
[chapter]

1991
*
Lecture Notes in Computer Science
*

We survey lower

doi:10.1007/3-540-54458-5_49
fatcat:tqfisfl5uba73egddzmtaoamwu
*bounds*established for*the*complexity*of*computing explicitly given*Boolean**functions*by switching-and-rectifier networks, branching programs and switching networks. ... Among these are monotone networks,*bounded*-width devices * ,*oblivious*devices and read-k times only devices. * we will be using*the*word "device" to denote*one**of**the*two words "program" and "network" ... Introduction*The*main goal*of**the**Boolean*complexity theory is to prove lower*bounds**on**the*complexity*of*computing "explicitly given"*Boolean**functions*in interesting computational models. ...##
###
The Random-Query Model and the Memory-Bounded Coupon Collector

2020
*
Innovations in Theoretical Computer Science
*

We study a new model

doi:10.4230/lipics.itcs.2020.20
dblp:conf/innovations/RazZ20
fatcat:23lbsxrrhbeyvjtozfwz2mkvle
*of*space-*bounded*computation,*the*random-query model.*The*model is based*on*a branching-program over input variables x1, . . . , xn. ... More precisely, a zero-error computation is a computation that stops with high*probability*and such that conditioning*on**the*event that*the*computation stopped,*the*output is correct with*probability*1 ... Let f be a*boolean**function**on*n-bits with sensitivity Ω(n) (For instance, AND, XOR, Majority, s-t connectivity, etc.). ...##
###
Is There an Oblivious RAM Lower Bound?

2016
*
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
*

We revisit

doi:10.1145/2840728.2840761
dblp:conf/innovations/BoyleN16
fatcat:2tsbwudqpjfdxf5xnkcmqvkpfi
*the*lower*bound**on**the*overhead required to*obliviously*simulate programs, due to Goldreich and Ostrovsky. ... Upon closer observation, however,*one*begins to see that*the*lower*bound**of*[GO96] is not*the*end*of**the*story. ... proving yet unknown circuit lower*bounds**on**the*size*of**Boolean*sorting circuits. ...##
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A communication game related to the sensitivity conjecture
[article]

2015
*
arXiv
*
pre-print

*One*

*of*

*the*major outstanding foundational problems about

*boolean*

*functions*is

*the*sensitivity conjecture, which (in

*one*

*of*its many forms) asserts that

*the*degree

*of*a

*boolean*

*function*(i.e.

*the*minimum ... There is an easy upper

*bound*

*of*√(n)

*on*

*the*cost

*of*

*the*game. We also improve slightly

*on*this upper

*bound*. ...

*The*second author was supported in part by (FP7/2007-2013)/ERC Consolidator grant LBCAD no. 616787, a grant from Neuron Fund for Support

*of*Science, and

*the*project 14-10003S

*of*GAČR. ...

##
###
Meanders, Ramsey theory and lower bounds for branching programs

1986
*
27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
*

A novel technique for obtaining lower

doi:10.1109/sfcs.1986.31
dblp:conf/focs/AlonM86
fatcat:esfwphmryfac7n5vwrq6sfruqi
*bounds*for*the*time versus space comp1exity*of*certain*functions*in a general input*oblivious*sequential model*of*computation is developed. ... This is demonstrated by studying*the*intrinsic complexity*of**the*following set equality problem SE(n,m): Given a sequence x 1 ,x 2 ,· .• ,x n ' Yl'·· .' ... All lower*bounds**on**the*length*of*input*oblivious*branching programs imply lower*bounds**on**the*number*of*steps that are needed to pebble arbitra~computation graphs for*the*same prob~m. ...##
###
Do Distributed Differentially-Private Protocols Require Oblivious Transfer?

2016
*
International Colloquium on Automata, Languages and Programming
*

We prove that any protocol to compute

doi:10.4230/lipics.icalp.2016.29
dblp:conf/icalp/GoyalKMPS16
fatcat:vqqgb6zlrbhxzm6tbyva4ykkn4
*the**boolean*XOR*functionality*in a distributed differentially private manner with optimal accuracy and overwhelming*probability**of*agreement (*on**the*output) between ... We resolve this question in*the*affirmative for*the*class*of**boolean**functionalities*that contain an XOR embedded*on*adjacent inputs. • We construct a protocol implementing*oblivious*transfer from any ... Consider an optimally accurate differentially private evaluation*of**the**boolean*XOR*functionality*, where both parties agree*on**the*output with overwhelming*probability*. ...##
###
On Multipartition Communication Complexity
[chapter]

2001
*
Lecture Notes in Computer Science
*

A collection

doi:10.1007/3-540-44693-1_18
fatcat:up6zpucsknbklbxc3kbk6zj2ly
*of*such rectangles r 1 , . . . , r t with respect to Π is said to form a rectangle cover with respect to Π*of*a*boolean**function*f defined*on*X if f = r 1 ∨ · · · ∨ r t . ... As an example, we mention*the*situation for branching programs, where*the*first exponential lower*bounds**on**the*size using communication complexity have been for*the**oblivious*variant*of**the*model (Alon ... Thus*the**bound**on**the*number*of*paths*of*length two and three is exceeded with*probability*at most 1/16. ...##
###
Page 6317 of Mathematical Reviews Vol. , Issue 93k
[page]

1993
*
Mathematical Reviews
*

Our main result is a (tight) linear lower

*bound**on**the*randomized decision tree comlexity*of*any*function*in RO-TC®. ... Several exponential lower*bounds**on**the*width*of*linear length*bounded**oblivious*parity branching programs are obtained and so also for*the*graph accessibility prob- lem*of*directed graphs, and*the*word ...##
###
On multi-partition communication complexity

2004
*
Information and Computation
*

A collection

doi:10.1016/j.ic.2004.05.002
fatcat:omgqvptmdfcctf5nmbs32xbnhi
*of*such rectangles r 1 , . . . , r t with respect to Π is said to form a rectangle cover with respect to Π*of*a*boolean**function*f defined*on*X if f = r 1 ∨ · · · ∨ r t . ... As an example, we mention*the*situation for branching programs, where*the*first exponential lower*bounds**on**the*size using communication complexity have been for*the**oblivious*variant*of**the*model (Alon ... Thus*the**bound**on**the*number*of*paths*of*length two and three is exceeded with*probability*at most 1/16. ...##
###
Proximity Oblivious Testing and the Role of Invariances
[chapter]

2011
*
Lecture Notes in Computer Science
*

Our focus is

doi:10.1007/978-3-642-22670-0_19
fatcat:6ys3dpyplrcijje5nurrqtdhjy
*on**the*case that*the*property is characterized by a constant number*of*local conditions and a rich set*of*invariances. ... We show that, in*the*aforementioned models*of*testing graph properties, characterization by such invariant local conditions is closely related to proximity*oblivious*testing (as defined by Goldreich and ... Theorem 5.3 There exists a property, denoted P,*of**Boolean**functions*such that P satisfies*the*invariance condition but has no proximity*oblivious*tester. ...##
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Computing in fault tolerant broadcast networks and noisy decision trees

2009
*
Random structures & algorithms (Print)
*

We consider a fault tolerant broadcast network

doi:10.1002/rsa.20240
fatcat:wmanzr2jmrb5tchctnbi5vqka4
*of*n processors each holding*one*bit*of*information.*The*goal is to compute a given*Boolean**function**on**the*n bits. ... In each step, a processor may broadcast*one*bit*of*information. Each listening processor receives*the*bit that was broadcast with error*probability**bounded*by a fixed constant . ... At*the*beginning*of**the*operation, each processor has*one*bit.*The*goal is to compute a given*Boolean**function**on*all*the*bits.*The*complexity*of**the*protocol is*the*total number*of*broadcasts. ...##
###
Proximity Oblivious Testing and the Role of Invariances
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that, in

doi:10.1007/978-3-642-22935-0_49
fatcat:ejyevsq7grfujf2hyorefx6woq
*the*aforementioned models*of*testing graph properties, characterization by such invariant local conditions is closely related to proximity*oblivious*testing (as defined by Goldreich and ... Our framework generalizes two popular models*of*testing graph properties as well as*the*algebraic invariances studied by Kaufman and Sudan (STOC'08). ...*On**the**one*hand,*the*definition*of*proximity*oblivious*testers does not refer to any structure*of**the*underlying domain*of**functions*, and*the*local conditions in*the*two graph models do not refer explicitly ...
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