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Ordered Functional Decision Diagrams: A Functional Semantics For Binary Decision Diagrams [article]

Joan Thibault, Khalil Ghorbal
2020 arXiv   pre-print
We introduce a novel framework, termed λDD, that revisits Binary Decision Diagrams from a purely functional point of view.  ...  The framework allows to classify the already existing variants, including the most recent ones like Chain-DD and ESRBDD, as implementations of a special class of ordered models.  ...  Ordered Functional Decision Diagrams We introduce a new data structure, akin to ordered BDD, that we term Ordered Functional Decision Diagram or λDD-O.  ... 
arXiv:2003.09340v4 fatcat:fkafwperdfgejdnk6uys6tvz64

Secure function evaluation with ordered binary decision diagrams

Louis Kruger, Somesh Jha, Eu-Jin Goh, Dan Boneh
2006 Proceedings of the 13th ACM conference on Computer and communications security - CCS '06  
Specifically we use the graph-based representation called ordered binary decision diagrams (OBDDs).  ...  For a large number of Boolean functions, OBDDs are more succinct than the gate-based representation.  ...  ORDERED BINARY DECISION DIAGRAMS (OBDDS) Ordered binary decision diagrams (OBDDs) are a canonical representation for Boolean formulas [3] .  ... 
doi:10.1145/1180405.1180455 dblp:conf/ccs/KrugerJGB06 fatcat:x7jw3flb7nan3jznykx36xrxme

Size of ordered binary decision diagrams representing threshold functions

K. Hosaka, Y. Takenaga, T. Kaneda, S. Yajima
1997 Theoretical Computer Science  
An ordered binary decision diagram (OBDD) is a graph representation of a Boolean function. In this paper, the size of ordered binary decision diagrams representing threshold functions is discussed.  ...  We also show some relations between the variable ordering and the size of OBDDs representing threshold functions.  ...  Ordered binary decision diagram (OBDLI) An ordered binary decision diagram (OBDD) [ 1,3] is a directed acyclic graph that represents a Boolean function.  ... 
doi:10.1016/s0304-3975(97)83807-8 fatcat:lj7zdgyadbalpowtap5ps2blzq

Binary Decision Diagrams: An Improved Variable Ordering Using Graph Representation Of Boolean Functions

P.W. C. Prasad, A. Assi, A. Harb, V.C. Prasad
2008 Zenodo  
This paper presents an improved variable ordering method to obtain the minimum number of nodes in Reduced Ordered Binary Decision Diagrams (ROBDD).  ...  The proposed method uses the graph topology to find the best variable ordering. Therefore the input Boolean function is converted to a unidirectional graph.  ...  Definition 2.4: A reduced ordered binary decision diagram (ROBDD) is an OBDD where each node represents a distinct logic function.  ... 
doi:10.5281/zenodo.1062259 fatcat:mvba5z35czgtdgdd4iyfvuh5qq

On the size of ordered binary decision diagrams representing threshold functions [chapter]

Kazuhisa Hosaka, Yasuhiko Takenaga, Shuzo Yajima
1994 Lecture Notes in Computer Science  
In this paper, the size of ordered binary decision diagrams representing threshold functions is studied.  ...  An ordered binary decision diagram (OBDD) is a graph representation of a Boolean function. It is observed that many practical Boolean functions are represented in feasible size.  ...  An ordered binary decision diagram (OBDD) [1] is a directed graph representing a Boolean function, and it is considered as one of the restricted types of branching programs.  ... 
doi:10.1007/3-540-58325-4_226 fatcat:ttf2pbxhjzbtvooctntio62m2q

Comparing two-level and ordered binary decision diagram representations of logic functions

S. Devadas
1993 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Abstmet-We give an example of a class of functions with 2n + log (n) inputs that have two-level or sum-of-products representations containing n2 product terms and ordered binary decision diagram representations  ...  that have at least Q(t"/*) vertices under any possible variable ordering.  ...  DEFINITIONS For standard logic synthesis and ordered binary decision diagram (OBDD) terminology, the reader is referred to [l] and [2] respectively.  ... 
doi:10.1109/43.277617 fatcat:bnelsengija5xkkgdkkfdch2ty

Forward and inverse transformations between Haar spectra and ordered binary decision diagrams of Boolean functions

B.J. Falkowski, Chip-Hong Chang
1997 IEEE transactions on computers  
Unnormalized Haar spectra and Ordered Binary Decision Diagrams (OBDDs) are two standard representations of Boolean functions used in logic design.  ...  The decomposition of the Haar spectrum, in terms of the cofactors of Boolean functions, has been introduced.  ...  An Ordered Binary Decision Diagram (OBDD) is a BDD where the input variables in all paths appear in a fixed order, and each variable in a path appears, at most, once.  ... 
doi:10.1109/12.644301 fatcat:pkpcbrvamzbsdoaorkzdqlisvm

Ordered Kronecker functional decision diagrams-a data structure for representation and manipulation of Boolean functions

R. Drechsler, B. Becker
1998 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
OKFDD's are a generalization of ordered binary decision diagrams (OBDD's) and ordered functional decision diagrams and thus combine the advantages of both.  ...  Ordered Kronecker functional decision diagrams (OKFDD's) are a data structure for efficient representation and manipulation of Boolean functions.  ...  If ease of manipulation and canonicity is not a main concern, still other types of decision diagrams, like ternary decision diagrams [28] and (free) Kronecker functional decision diagrams [20] , have  ... 
doi:10.1109/43.728917 fatcat:2jfrtl3h4jevdbvz4gsjawuqpu

Synthesis for testability: circuits derived from ordered Kronecker functional decision diagrams

B. Becker, R. Drechsler
Proceedings the European Design and Test Conference. ED&TC 1995  
Testability properties of circuits derived f r om Ordered K r onecker Functional Decision Diagrams (OKFDDs) [2] a r e studied with respect to the Stuck-At F ault Model (SAFM) and the Cellular Fault Model  ...  Our experiments for some of the LGSynth91 benchmarks show that OKFDD-circuits provide a more compact realization of Boolean functions than OBDD-or OFDD-circuits.  ...  An OKFDD-circuit can easily be obtained from an OKFDD by traversing the corresponding graph in topological order and replacing all nodes by the corresponding cells from the library.  ... 
doi:10.1109/edtc.1995.470336 dblp:conf/date/BeckerD95a fatcat:dzibguxjtfha7ne4nr4sjwhgky

Implementation of GA with Position Based Crossover-PX Technique for Size Optimization of BDD Mapped Adder Circuits

2020 International Journal of Engineering and Advanced Technology  
Binary Decision Diagrams or BDD are data structure used to represent single and multi-output digital circuits.  ...  BDD mapped adder circuits are used to represent different adder functions in a digital system. Optimization of adder circuits are done by optimizing the corresponding BDDs.  ...  is known as Reduced and Ordered Binary decision Diagram [4] .  ... 
doi:10.35940/ijeat.c6358.029320 fatcat:nasm4v5ozfamvlmuasabkfyi4u

On an optimization technique using Binary Decision Diagram [article]

Debajit Sensarma, Subhashis Banerjee, Krishnendu Basuli, Saptarshi Naskar, Samar Sen Sarma
2012 arXiv   pre-print
This paper represents a method of minimizing Boolean sum of products function with binary decision diagram and with disjoint sum of product minimization.  ...  The application of Binary Decision Diagrams (BDDs) as an efficient approach for the minimization of Disjoint Sums-of-Products (DSOPs). DSOPs are a starting point for several applications.  ...  Decision Diagram isFinding Disjoint Cubes from Above Binary Decision Diagram.  ... 
arXiv:1203.2505v1 fatcat:hgdmt6q5afeelncmtizshb4vue

Practical modeling of Bayesian decision problems - exploiting deterministic relations

A.L. Madsen, K.G. Olesen, S.L. Dittmer
2002 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
In this paper, we propose a number of extensions and adjustments to the definition of influence diagrams in order to make the practical use of influence diagrams more flexible and less restrictive.  ...  The widespread use of influence diagrams to represent and solve Bayesian decision problems is still limited by the inflexibility and rather restrictive semantics of influence diagrams.  ...  Uncertain Information Arcs The information arcs of an influence diagram indicate the order in which information becomes available to the decision maker.  ... 
doi:10.1109/3477.979957 pmid:18238101 fatcat:2dfpi7xa6zc63fzrqfwzopgsvi

Decision diagrams in machine learning: an empirical study on real-life credit-risk data

Christophe Mues, Bart Baesens, Craig M. Files, Jan Vanthienen
2004 Expert systems with applications  
Alternatively, decision diagrams, a generalization of decision trees taking on the form of a rooted, acyclic digraph instead of a tree, have occasionally been suggested as a potentially more compact representation  ...  Therefore, in this paper, starting from a series of rule sets extracted from three real-life credit-scoring data sets, we will empirically assess to what extent decision diagrams are able to provide a  ...  When using decision diagrams to represent a function, some total ordering of the input variables must be selected.  ... 
doi:10.1016/j.eswa.2004.02.001 fatcat:kf46majsdvgd3g4kknk5udy3mi

Decision Diagrams in Machine Learning: An Empirical Study on Real-Life Credit-Risk Data [chapter]

Christophe Mues, Bart Baesens, Craig M. Files, Jan Vanthienen
2004 Lecture Notes in Computer Science  
Alternatively, decision diagrams, a generalization of decision trees taking on the form of a rooted, acyclic digraph instead of a tree, have occasionally been suggested as a potentially more compact representation  ...  Therefore, in this paper, starting from a series of rule sets extracted from three real-life credit-scoring data sets, we will empirically assess to what extent decision diagrams are able to provide a  ...  When using decision diagrams to represent a function, some total ordering of the input variables must be selected.  ... 
doi:10.1007/978-3-540-25931-2_49 fatcat:jteqm2iyj5gkvccnnsegryu5tu

Ordered binary decision diagrams and minimal trellises

J. Lafferty, A. Vardy
1999 IEEE transactions on computers  
We would like to thank Randy Bryant for several helpful and informative discussions on binary decision diagrams.  ...  Biproper binary decision diagrams. Let V be an ordered binary decision diagram for a Boolean function f(xi,...,x n ).  ...  Construction of ordered binary decision diagrams A binary decision diagram represents a Boolean function as a rooted, directed acyclic graph.  ... 
doi:10.1109/12.795225 fatcat:72as4nzt7bbifhbgtvlab3ertu
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