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Oblivious bounds on the probability of boolean functions

Wolfgang Gatterbauer, Dan Suciu
2014 ACM Transactions on Database Systems  
This paper develops upper and lower 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/.  ... 
doi:10.1145/2532641 fatcat:6lehdkydyndzflh7rkerohgelq

Making Branching Programs Oblivious Requires Superlogarithmic Overhead

Paul Beame, Widad Machmouchi
2011 2011 IEEE 26th Annual Conference on Computational Complexity  
These are also 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.  ... 
doi:10.1109/ccc.2011.35 dblp:conf/coco/BeameM11 fatcat:llp2k6z6g5gwxhql6d3vwgz5qa

Meanders and their applications in lower bounds arguments

Noga Alon, Wolfgang Maasst
1988 Journal of computer and system sciences (Print)  
In particular, an Q (n log n) lower 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  ... 
doi:10.1016/0022-0000(88)90002-5 fatcat:c5gyqtmzurcctnugwnrql2n5ja

Lower bounds for deterministic and nondeterministic branching programs [chapter]

Alexander A. Razborov
1991 Lecture Notes in Computer Science  
We survey lower 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.  ... 
doi:10.1007/3-540-54458-5_49 fatcat:tqfisfl5uba73egddzmtaoamwu

The Random-Query Model and the Memory-Bounded Coupon Collector

Ran Raz, Wei Zhan, Michael Wagner
2020 Innovations in Theoretical Computer Science  
We study a new model 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.).  ... 
doi:10.4230/lipics.itcs.2020.20 dblp:conf/innovations/RazZ20 fatcat:23lbsxrrhbeyvjtozfwz2mkvle

Is There an Oblivious RAM Lower Bound?

Elette Boyle, Moni Naor
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
We revisit 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.  ... 
doi:10.1145/2840728.2840761 dblp:conf/innovations/BoyleN16 fatcat:2tsbwudqpjfdxf5xnkcmqvkpfi

A communication game related to the sensitivity conjecture [article]

Justin Gilmer, Michal Koucký, Michael Saks
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.  ... 
arXiv:1511.07729v1 fatcat:3qcibujuczhhxhenplqsgrev7u

Meanders, Ramsey theory and lower bounds for branching programs

Noga Alon, Wolfgang Maass
1986 27th Annual Symposium on Foundations of Computer Science (sfcs 1986)  
A novel technique for obtaining lower 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.  ... 
doi:10.1109/sfcs.1986.31 dblp:conf/focs/AlonM86 fatcat:esfwphmryfac7n5vwrq6sfruqi

Do Distributed Differentially-Private Protocols Require Oblivious Transfer?

Vipul Goyal, Dakshita Khurana, Ilya Mironov, Omkant Pandey, Amit Sahai, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
We prove that any protocol to compute 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.  ... 
doi:10.4230/lipics.icalp.2016.29 dblp:conf/icalp/GoyalKMPS16 fatcat:vqqgb6zlrbhxzm6tbyva4ykkn4

On Multipartition Communication Complexity [chapter]

Pavol Ďuriš, Juraj Hromkovič, Stasys Jukna, Martin Sauerhoff, Georg Schnitger
2001 Lecture Notes in Computer Science  
A collection 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.  ... 
doi:10.1007/3-540-44693-1_18 fatcat:up6zpucsknbklbxc3kbk6zj2ly

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

Pavol Ďuriš, Juraj Hromkovič, Stasys Jukna, Martin Sauerhoff, Georg Schnitger
2004 Information and Computation  
A collection 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.  ... 
doi:10.1016/j.ic.2004.05.002 fatcat:omgqvptmdfcctf5nmbs32xbnhi

Proximity Oblivious Testing and the Role of Invariances [chapter]

Oded Goldreich, Tali Kaufman
2011 Lecture Notes in Computer Science  
Our focus is 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.  ... 
doi:10.1007/978-3-642-22670-0_19 fatcat:6ys3dpyplrcijje5nurrqtdhjy

Computing in fault tolerant broadcast networks and noisy decision trees

Ilan Newman
2009 Random structures & algorithms (Print)  
We consider a fault tolerant broadcast network 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.  ... 
doi:10.1002/rsa.20240 fatcat:wmanzr2jmrb5tchctnbi5vqka4

Proximity Oblivious Testing and the Role of Invariances [chapter]

Oded Goldreich, Tali Kaufman
2011 Lecture Notes in Computer Science  
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  ...  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  ... 
doi:10.1007/978-3-642-22935-0_49 fatcat:ejyevsq7grfujf2hyorefx6woq
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