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Approximating Boolean functions by OBDDs

2007
*
Discrete Applied Mathematics
*

In learning theory and genetic programming,

doi:10.1016/j.dam.2006.04.037
fatcat:krcsn4gakfafzlay6kzhd5ss4i
*OBDDs*are used to represent*approximations*of*Boolean**functions*. ... Using this new type of reduction, we prove the following results on*OBDD**approximations*of*Boolean**functions*: 1. ... Motivated*by*these applications, Krause, Savický and Wegener [4] started investigating lower bounds on the size of*OBDDs**approximating**Boolean**functions*. Definition 2. ...##
###
Approximating Boolean Functions by OBDDs
[chapter]

2004
*
Lecture Notes in Computer Science
*

In learning theory and genetic programming,

doi:10.1007/978-3-540-28629-5_17
fatcat:p3xsjn73dvghbaklk2q4twztmi
*OBDDs*are used to represent*approximations*of*Boolean**functions*. ... Using this new type of reduction, we prove the following results on*OBDD**approximations*of*Boolean**functions*: 1. ... Motivated*by*these applications, Krause, Savický and Wegener [4] started investigating lower bounds on the size of*OBDDs**approximating**Boolean**functions*. Definition 2. ...##
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What Graphs can be Efficiently Represented by BDDs?

2007
*
2007 International Conference on Computing: Theory and Applications (ICCTA'07)
*

We have carried out experimental research into implicit representation of large graphs using reduced ordered binary decision diagrams (

doi:10.1109/iccta.2007.133
dblp:conf/iccta/DongM07
fatcat:v4lozcczkzbtno4xeprtviwgda
*OBDDs*). ... For randomly generated dense graphs, the gain, i. e., the ratio of the number of graph edges to the*OBDD*size, increases with the number of vertices and the density of the graphs. ... Introduction Reduced ordered binary decision diagram (*OBDD*) is a canonical method to represent*Boolean**functions*[3] . ...##
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Distributed Hybrid Genetic Programming for Learning Boolean Functions
[chapter]

2000
*
Lecture Notes in Computer Science
*

Here, the first GP-system is presented that evolves the variable ordering of the

doi:10.1007/3-540-45356-3_18
fatcat:5wyfqbgwsfdrbg7cmez7m2txca
*OBDDs*and the*OBDDs*itself*by*using a distributed hybrid approach. ... Hence, this approach is a big step towards learning well-generalizing*Boolean**functions*. ... Hence, the representation of*Boolean**functions**by*reduced*OBDDs*eliminates redundant code and automatically discovers useful subfunctions in a similar manner as automatically defined*functions*( [8] ) ...##
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Boolean resubstitution with permissible functions and binary decision diagrams

1990
*
Conference proceedings on 27th ACM/IEEE design automation conference - DAC '90
*

We represent the data structure of permissible

doi:10.1145/123186.123276
dblp:conf/dac/SatoYMF90
fatcat:62yah3qqsnf2pp53k6bwauv5yu
*functions*and logic*functions*at each node in*Boolean*networks in terms of*OBDD*. ... In this paper, we present a new*Boolean*resubstitution technique with permissible*functions*and ordered binary decision diagrams, abbreviated as*OBDD*[8] . ... When there are two*Boolean**functions*such as the followingfand g. f is substituted with g*by**Boolean*resubstitution. ...##
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Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard
[chapter]

2006
*
Lecture Notes in Computer Science
*

*by*Pitt and Warmuth [11] and Simon [14] for deterministic finite automata, a model closely related to

*OBDDs*. ... We present an efficient reduction mapping undirected graphs G with n = 2 k vertices for integers k to tables of partially specified

*Boolean*

*functions*g : {0, 1} 4k+1 → {0, 1, ⊥} so that for any integer ... The research of Peter Bro Miltersen was supported

*by*BRICS, a center of the Danish National Research Foundation and

*by*a grant from the Danish Science Research Council. ...

##
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Hardness of identifying the minimum ordered binary decision diagram

2000
*
Discrete Applied Mathematics
*

An ordered binary decision diagram (

doi:10.1016/s0166-218x(99)00226-7
fatcat:5mjpej5qbncmrpuiyyl63w3iku
*OBDD*) is a graph representation of a*Boolean**function*. ... We consider minimum*OBDD*identiÿcation problems: given positive and negative examples of a*Boolean**function*, identify the*OBDD*with minimum number of nodes (or with minimum width) that is consistent with ... It is known that a*Boolean**function*is uniquely represented*by*a reduced*OBDD*or a quasi-reduced*OBDD*, provided that the variable ordering is ÿxed. ...##
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On the Nonapproximability of Boolean Functions by OBDDs and Read-k-Times Branching Programs

2002
*
Information and Computation
*

For learning

doi:10.1006/inco.2002.3174
fatcat:5w23ftty6vhvrpfnrwjnsyk6cu
*boolean**functions*f on the basis of classified examples, it is sufficient to produce the representation of a*function*g*approximating*f . ... with respect to the uniform distribution*by**OBDDs*, which are the most important type of branching programs in applications. (2) The first truly exponential lower bound on the size of*approximating*syntactic ... Obviously, each*boolean**function*is*approximated*with error probability 1/2*by*one of the two constant*functions*. ...##
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On the influence of the variable ordering for algorithmic learning using OBDDs

2005
*
Information and Computation
*

In this paper, it is shown that, for some

doi:10.1016/j.ic.2005.05.004
fatcat:zbegq7yojffkpo3xes6afcfe5m
*functions*, it is necessary to develop an algorithm to learn also a good*OBDD*variable ordering. There are*functions*with the following properties. ... These properties are shown for simple*functions*like the multiplexer and the inner product. ...*Approximability**by**OBDDs*and genetic programming We denote*by*B n the set of all*Boolean**functions*f : {0, 1} n → {0, 1}. ...##
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Learning ordered binary decision diagrams
[chapter]

1995
*
Lecture Notes in Computer Science
*

This note studies the learnability of ordered binary decision diagrams (

doi:10.1007/3-540-60454-5_41
fatcat:p54oje5hdbhojenmhnxi6iy32q
*obdds*). ... ordering for a given*obdd*and the Optimal Linear Arrangement problem on graphs. ... Theorem 18 If*boolean**functions*are learnable in terms of*obdds*(with respect to the best ordering, but not necessarily in minimal form) then OLA can be*approximated*within a polynomial. Proof. ...##
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Inapproximability of a Pair of Forms Defining a Partial Boolean Function
[article]

2022
*
arXiv
*
pre-print

We hypothesize that this problem is easier to solve or

arXiv:2102.04703v3
fatcat:md37tq26ljajnex4whcnwmjbp4
*approximate*than the well-understood problem of minimizing the form of one*Boolean**function*h: {0,1}^J →{0,1} such that h(A) = {1} and h(B) = {0}. ... We consider the problem of jointly minimizing forms of two*Boolean**functions*f, g {0,1}^J →{0,1} such that f + g ≤ 1 and so as to separate disjoint sets A ∪ B ⊆{0,1}^J such that f(A) = {1} and g(B) = { ... Our work is motivated*by*the hypothesis that the problem of learning a partial*Boolean**function*is easier to solve or*approximate*than the problem of learning a (total)*Boolean**function*. ...##
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Interpretability of Bayesian Network Classifiers: OBDD Approximation and Polynomial Threshold Functions

2020
*
International Symposium on Artificial Intelligence and Mathematics
*

The

dblp:conf/isaim/ChubarianT20
fatcat:mcrmtibnhjghbfvwakbu76a2km
*OBDD**approximation*algorithm applies to any such*Boolean**function*and any distribution which can be*approximated**by*a polynomial-width distribution. ... We study the*approximability*of Bayesian network classifiers*by*Ordered Binary Decision Diagrams (*OBDD*). This generalizes an approach introduced*by*Chan and Darwiche. ...*OBDD*and GOBDD An ordered binary decision diagram (*OBDD*) over*Boolean*variables x 1 , . . . , x n computes a*Boolean**function*f . ...##
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Improving NFA-Based Signature Matching Using Ordered Binary Decision Diagrams
[chapter]

2010
*
Lecture Notes in Computer Science
*

Experiments using Snort HTTP and FTP signature sets show that an NFA-

doi:10.1007/978-3-642-15512-3_4
fatcat:en3icdjxtnc7lns4b4ase3zhye
*OBDD*-based representation of regular expressions can outperform traditional NFAs*by*up to three orders of magnitude and is competitive ... This paper presents NFA-*OBDDs*, a symbolic representation of NFAs that retains their space-efficiency while improving their time-efficiency. ...*OBDDs*allow*Boolean**functions*to be manipulated efficiently. ...##
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On the hardness of approximating the minimum consistent OBDD problem
[chapter]

1996
*
Lecture Notes in Computer Science
*

Ordered binary decision diagrams (

doi:10.1007/3-540-61422-2_125
fatcat:r6kf25ide5hspmvcdp2zgdmrlu
*OBDD*, for short) represent*Boolean**functions*as directed acyclic graphs. ... Furthermore, we g i v e a polynomial time learnable subclass of*OBDDs*representing symmetric*functions*. ... Many useful*Boolean**functions*, such as symmetric*functions*and threshold*functions*, can be expressed succinctly*by**OBDDs*[9] . ...##
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Fast, memory-efficient regular expression matching with NFA-OBDDs

2011
*
Computer Networks
*

Experiments using HTTP and FTP signature sets from Snort show that NFA-

doi:10.1016/j.comnet.2011.07.002
fatcat:xw7ngkos5zcn5jl26kwnv3cfd4
*OBDDs*can outperform traditional NFAs*by*up to three orders of magnitude, thereby making them competitive with a variant of DFAs, ... We introduce NFA-*OBDDs*, which use ordered binary decision diagrams (*OBDDs*) to efficiently process sets of NFA frontier states. ... This work was supported in part*by*NSF Grants 0831268, 0915394, 0931992 and 0952128. ...
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