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A Generalization of the Noisy-Or Model
[chapter]

1993
*
Uncertainty in Artificial Intelligence
*

Here we generalize the model to nary

doi:10.1016/b978-1-4832-1451-1.50030-5
fatcat:gpvdg2wqcramnm7fhazz2btnaq
*input*and output variables and to ar bitrary*functions*other than the*Boolean*OR*function*. ... The*Noisy*-Or model is convenient for de scribing a class of uncertain relationships in Bayesian networks [Pearl 1988 ]. Pearl describes the*Noisy*-Or model for*Boolean*variables. ... We now suggest a particular form of F that is 'compat ible'*with*the*Boolean**Noisy*-Or, i.e., F degenerates to the*Boolean*OR*function*when the*inputs*and outputs are Boolean23: In essence, this*function*...##
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Reliable computation from contextual correlations

2017
*
Physical Review A
*

Here we investigate the requirements for reliable computation in this setting, that is, the evaluation of any

doi:10.1103/physreva.96.062305
fatcat:6b6rchgpundpxp4yajvkvf3cee
*Boolean**function**with*success probability bounded away from 1/2. ...*functions*. ... An ǫ-*noisy*, k-*input*gate computes a k-bit*Boolean**function*, outputting the correct answer*with*probability 1−ǫ, and its negation*with*probability ǫ, independently of the*input*. ...##
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On networks of noisy gates

1985
*
26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
*

This may be contrasted

doi:10.1109/sfcs.1985.41
dblp:conf/focs/Pippenger85
fatcat:jgxs3x4gyve77ngx6sbnfoarie
*with*results of von Neumann, Dobrushin and Ortyukov to the effect that (1) for every*Boolean**function*, the number of*noisy*gates needed is larger by at most a logarithmic factor, ... We show that many*Boolean**functions*(including, in a certain sense, "almost all"*Boolean**functions*) have the . property that the number of*noisy*gates needed to compute them differs from the number of ... We shall take e=I/512, 8=1/128 and show that the*noisy*network strongly (E, B)-computes the same*function*as the noiseless one. Let A be a set of xm*inputs**with*xs 1/64. ...##
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On the maximum tolerable noise of k-input gates for reliable computation by formulas

2003
*
IEEE Transactions on Information Theory
*

We determine the precise threshold of component noise below which formulas composed of odd degree components can reliably compute all

doi:10.1109/tit.2003.818405
fatcat:tw7bp3v3gbhzjpzmvqxkdkxyje
*Boolean**functions*. ... An -*noisy*gate computes a*Boolean**function*of its*inputs*that is then complemented*with*probability to become the gate's output. ... An -*noisy*, k-*input*gate is designed to compute a*Boolean**function*of its k*Boolean**inputs*; however, it has the property that for any assignment to the*inputs*, there is probability that the output of the ...##
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Average-Case Lower Bounds for Noisy Boolean Decision Trees

1998
*
SIAM journal on computing (Print)
*

We present a new method for deriving lower bounds to the expected number of queries made by

doi:10.1137/s0097539796310102
fatcat:4cl5eexgqjeynaearqv6es27ze
*noisy*decision trees computing*Boolean**functions*. ... The new method has the feature that expectations are taken*with*respect to a uniformly distributed random*input*, as well as*with*respect to the random noise, thus yielding stronger lower bounds. ... Suppose that the*noisy*dynamic decision tree T (ε, δ)-computes the*Boolean**function*f*with*expected cost C averaged over both*inputs*and noise. Let δ be such that δ < δ < 1/2. ...##
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Computing with Noise: Phase Transitions in Boolean Formulas

2009
*
Physical Review Letters
*

Computing circuits composed of

doi:10.1103/physrevlett.103.248701
pmid:20366241
fatcat:yfkpd6zzrfdnfbb2doehp5ox3u
*noisy*logical gates and their ability to represent arbitrary*Boolean**functions**with*a given level of error are investigated within a statistical mechanics setting. ... This framework paves the way for obtaining new results on error-rates,*function*-depth and sensitivity, and their dependence on the gate-type and noise model used. ... A*noisy*circuit*with*> 0 represents a given deterministic*function**with*a maximum error probability δ over all possible circuit*inputs*determining its reliability. ...##
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On the maximum tolerable noise for reliable computation by formulas

1991
*
IEEE Transactions on Information Theory
*

*Boolean*

*function*, the network required for the proof is described as follows. Start

*with*a formula for computing the

*function*using only noiseless 2-

*input*NAND gates. ... Consider a

*Boolean*

*function*F of at least 1 + 3'--l essential arguments, and consider any formula constructed of e-

*noisy*3-

*input*gates for computing F. ...

##
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On the robustness of random Boolean formulae

2010
*
Journal of Physics, Conference Series
*

Random

doi:10.1088/1742-6596/233/1/012015
fatcat:flz53sg3mbfu7mxkqbljemayu4
*Boolean*formulae, generated by a growth process of*noisy*logical gates are analyzed using the generating*functional*methodology of statistical physics. ... We study the type of*functions*generated for different*input*distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. ... (iii) The -*noisy*gate is designed to compute a*Boolean**function*α : {−1, 1} k → {−1, 1}, but for each*input*S ∈ {−1, 1} k there is an error probability such that α(S) → −α(S). ...##
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On reliable computation by noisy random Boolean formulas
[article]

2014
*
arXiv
*
pre-print

We show that these gates can be used to compute any

arXiv:1206.4851v2
fatcat:twb6jagzwfeajc4ozifi3qw3by
*Boolean**function*reliably below the noise bound. ... We study*noisy*computation in randomly generated k-ary*Boolean*formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. ... The ǫ-*noisy*gate is designed to compute a*Boolean**function*α(σ), but for each*input*σ ∈ {−1, 1} k there is an error probability ǫ such that α(σ) → −α(σ). ...##
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Do Distributed Differentially-Private Protocols Require Oblivious Transfer?

2016
*
International Colloquium on Automata, Languages and Programming
*

optimally accurate, distributed differentially private protocol for any

doi:10.4230/lipics.icalp.2016.29
dblp:conf/icalp/GoyalKMPS16
fatcat:vqqgb6zlrbhxzm6tbyva4ykkn4
*functionality**with*a*boolean*XOR embedded on adjacent*inputs*. • While the previous result holds for optimally accurate protocols ... This is because the output of the*functionality*combined*with*the*input*of any individual party reveals completely, the*input*of the other party. ... Alice and Bob,*with**inputs*x and y respectively, execute a protocol to compute a*Boolean**function*f (x, y). ...##
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The Complexity of Combinatorial Computations: An Introduction
[chapter]

1978
*
Informatik-Fachberichte
*

*Noisy*Decision Trees An -

*noisy*decision tree on N

*boolean*

*input*variables is a decision tree where each internal node is labelled by one of the N

*input*variables and each leaf is labelled by a

*boolean*... One of them is to find interesting

*boolean*

*functions*that need superlinear number of broadcasts in the

*noisy*broadcast model

*with*random noise. ...

##
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On Reliable Computation by Noisy Random Boolean Formulas

2015
*
IEEE Transactions on Information Theory
*

We show that these gates can be used to compute any

doi:10.1109/tit.2014.2370638
fatcat:ah7bqncpq5bpjfb2wlumplkx7a
*Boolean**function*reliably below the noise bound. Index Terms-Random*Boolean*formulas, ǫ-noise, reliable computation. ... We study*noisy*computation in randomly generated k-ary*Boolean*formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. ... Thus in this regime any*Boolean**function*can be computed*with*any desired accuracy. III. ...##
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ATEN: And/Or tree ensemble for inferring accurate Boolean network topology and dynamics

2019
*
Bioinformatics
*

Using these important features we then infer the

doi:10.1093/bioinformatics/btz563
pmid:31368481
fatcat:sla5fz3rkranfisldhoadilyf4
*Boolean**function*of the target gene. Finally, the*Boolean**functions*of all target genes are combined as a*Boolean*network. ... To address the problem, we propose a*Boolean*network inference algorithm which is able to infer accurate*Boolean*network topology and dynamics from short and*noisy*time series data. ... The directed edges, or the interactions between the target gene and*input*genes are associated*with*the regulatory rule, i.e., the*Boolean**function*. ...##
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Noisy random Boolean formulae: A statistical physics perspective

2010
*
Physical Review E
*

A growth model that gives rise to typical random

doi:10.1103/physreve.82.041112
pmid:21230243
fatcat:xrhkddzvgfewpjj5mvxshbajwi
*Boolean**functions*is mapped onto a layered Ising spin system, which facilitates the study of their ability to represent arbitrary formulae*with*a given ... level of error, the tolerable level of gate-noise, and its dependence on the formulae depth and complexity, the gates used and properties of the*function**inputs*. ... However, this strategy fails for*inputs**with*m͑0͒ = 0 and the circuit computes more than one*Boolean**function*. ...##
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On a lower bound for the redundancy of reliable networks with noisy gates

1991
*
IEEE Transactions on Information Theory
*

We provide a proof that a logarithmic redundancy factor is necessary for the reliable computation of the parity

doi:10.1109/18.79921
fatcat:nqjyuy3l7nasdeaaevulp6fs5u
*function*by means of a network*with**noisy*gates. ... We have established the result by following the same steps as Dobrushin and Ortyukov and by replacing the questionable part of their analysis*with*entirely new argumnents. ... INTRODUCTION Computation of*Boolean**functions*by means of*noisy*gates is a topic that started attracting the attention of researchers in the early '50s. ...
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