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Approximating Boolean functions by OBDDs

Andre Gronemeier
2007 Discrete Applied Mathematics  
In learning theory and genetic programming, 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.  ... 
doi:10.1016/j.dam.2006.04.037 fatcat:krcsn4gakfafzlay6kzhd5ss4i

Approximating Boolean Functions by OBDDs [chapter]

Andre Gronemeier
2004 Lecture Notes in Computer Science  
In learning theory and genetic programming, 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.  ... 
doi:10.1007/978-3-540-28629-5_17 fatcat:p3xsjn73dvghbaklk2q4twztmi

What Graphs can be Efficiently Represented by BDDs?

C. Dong, P. Molitor
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 (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] .  ... 
doi:10.1109/iccta.2007.133 dblp:conf/iccta/DongM07 fatcat:v4lozcczkzbtno4xeprtviwgda

Distributed Hybrid Genetic Programming for Learning Boolean Functions [chapter]

Stefan Droste, Dominic Heutelbeck, Ingo Wegener
2000 Lecture Notes in Computer Science  
Here, the first GP-system is presented that evolves the variable ordering of the 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] )  ... 
doi:10.1007/3-540-45356-3_18 fatcat:5wyfqbgwsfdrbg7cmez7m2txca

Boolean resubstitution with permissible functions and binary decision diagrams

Hitomi Sato, Yoshihiro Yasue, Yusuke Matsunaga, Masahiro Fujita
1990 Conference proceedings on 27th ACM/IEEE design automation conference - DAC '90  
We represent the data structure of permissible 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.  ... 
doi:10.1145/123186.123276 dblp:conf/dac/SatoYMF90 fatcat:62yah3qqsnf2pp53k6bwauv5yu

Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard [chapter]

Jesper Torp Kristensen, Peter Bro Miltersen
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.  ... 
doi:10.1007/11809678_51 fatcat:2nsco5zy5vgyzex3jsfzxjny6i

Hardness of identifying the minimum ordered binary decision diagram

Yasuhiko Takenaga, Shuzo Yajima
2000 Discrete Applied Mathematics  
An ordered binary decision diagram (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.  ... 
doi:10.1016/s0166-218x(99)00226-7 fatcat:5mjpej5qbncmrpuiyyl63w3iku

On the Nonapproximability of Boolean Functions by OBDDs and Read-k-Times Branching Programs

Beate Bollig, Martin Sauerhoff, Ingo Wegener
2002 Information and Computation  
For learning 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.  ... 
doi:10.1006/inco.2002.3174 fatcat:5w23ftty6vhvrpfnrwjnsyk6cu

On the influence of the variable ordering for algorithmic learning using OBDDs

Matthias Krause, Petr Savický, Ingo Wegener
2005 Information and Computation  
In this paper, it is shown that, for some 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}.  ... 
doi:10.1016/j.ic.2005.05.004 fatcat:zbegq7yojffkpo3xes6afcfe5m

Learning ordered binary decision diagrams [chapter]

Ricard Gavaldà, David Guijarro
1995 Lecture Notes in Computer Science  
This note studies the learnability of ordered binary decision diagrams (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.  ... 
doi:10.1007/3-540-60454-5_41 fatcat:p54oje5hdbhojenmhnxi6iy32q

Inapproximability of a Pair of Forms Defining a Partial Boolean Function [article]

David Stein, Bjoern Andres
2022 arXiv   pre-print
We hypothesize that this problem is easier to solve or 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.  ... 
arXiv:2102.04703v3 fatcat:md37tq26ljajnex4whcnwmjbp4

Interpretability of Bayesian Network Classifiers: OBDD Approximation and Polynomial Threshold Functions

Karine Chubarian, György Turán
2020 International Symposium on Artificial Intelligence and Mathematics  
The 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 .  ... 
dblp:conf/isaim/ChubarianT20 fatcat:mcrmtibnhjghbfvwakbu76a2km

Improving NFA-Based Signature Matching Using Ordered Binary Decision Diagrams [chapter]

Liu Yang, Rezwana Karim, Vinod Ganapathy, Randy Smith
2010 Lecture Notes in Computer Science  
Experiments using Snort HTTP and FTP signature sets show that an NFA-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.  ... 
doi:10.1007/978-3-642-15512-3_4 fatcat:en3icdjxtnc7lns4b4ase3zhye

On the hardness of approximating the minimum consistent OBDD problem [chapter]

Kouichi Hirata, Shinichi Shimozono, Ayumi Shinohara
1996 Lecture Notes in Computer Science  
Ordered binary decision diagrams (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] .  ... 
doi:10.1007/3-540-61422-2_125 fatcat:r6kf25ide5hspmvcdp2zgdmrlu

Fast, memory-efficient regular expression matching with NFA-OBDDs

Liu Yang, Rezwana Karim, Vinod Ganapathy, Randy Smith
2011 Computer Networks  
Experiments using HTTP and FTP signature sets from Snort show that NFA-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.  ... 
doi:10.1016/j.comnet.2011.07.002 fatcat:xw7ngkos5zcn5jl26kwnv3cfd4
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