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

2020
*
arXiv
*
pre-print

We introduce a novel framework, termed λDD, that revisits Binary

arXiv:2003.09340v4
fatcat:fkafwperdfgejdnk6uys6tvz64
*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. ...##
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Secure function evaluation with ordered binary decision diagrams

2006
*
Proceedings of the 13th ACM conference on Computer and communications security - CCS '06
*

Specifically we use the graph-based representation called

doi:10.1145/1180405.1180455
dblp:conf/ccs/KrugerJGB06
fatcat:x7jw3flb7nan3jznykx36xrxme
*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] . ...##
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Size of ordered binary decision diagrams representing threshold functions

1997
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Theoretical Computer Science
*

An

doi:10.1016/s0304-3975(97)83807-8
fatcat:lj7zdgyadbalpowtap5ps2blzq
*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*. ...##
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Binary Decision Diagrams: An Improved Variable Ordering Using Graph Representation Of Boolean Functions

2008
*
Zenodo
*

This paper presents an improved variable

doi:10.5281/zenodo.1062259
fatcat:mvba5z35czgtdgdd4iyfvuh5qq
*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*. ...##
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On the size of ordered binary decision diagrams representing threshold functions
[chapter]

1994
*
Lecture Notes in Computer Science
*

In this paper, the size of

doi:10.1007/3-540-58325-4_226
fatcat:ttf2pbxhjzbtvooctntio62m2q
*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. ...##
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Comparing two-level and ordered binary decision diagram representations of logic functions

1993
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

Abstmet-We give an example of a class of

doi:10.1109/43.277617
fatcat:bnelsengija5xkkgdkkfdch2ty
*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. ...##
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Forward and inverse transformations between Haar spectra and ordered binary decision diagrams of Boolean functions

1997
*
IEEE transactions on computers
*

Unnormalized Haar spectra and

doi:10.1109/12.644301
fatcat:pkpcbrvamzbsdoaorkzdqlisvm
*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. ...##
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Ordered Kronecker functional decision diagrams-a data structure for representation and manipulation of Boolean functions

1998
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

OKFDD's are a generalization of

doi:10.1109/43.728917
fatcat:2jfrtl3h4jevdbvz4gsjawuqpu
*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 ...##
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Synthesis for testability: circuits derived from ordered Kronecker functional decision diagrams

*
Proceedings the European Design and Test Conference. ED&TC 1995
*

Testability properties of circuits derived f r om

doi:10.1109/edtc.1995.470336
dblp:conf/date/BeckerD95a
fatcat:dzibguxjtfha7ne4nr4sjwhgky
*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. ...##
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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

doi:10.35940/ijeat.c6358.029320
fatcat:nasm4v5ozfamvlmuasabkfyi4u
*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] . ...##
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On an optimization technique using Binary Decision Diagram
[article]

2012
*
arXiv
*
pre-print

This paper represents a method of minimizing Boolean sum of products

arXiv:1203.2505v1
fatcat:hgdmt6q5afeelncmtizshb4vue
*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*. ...##
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Practical modeling of Bayesian decision problems - exploiting deterministic relations

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

doi:10.1109/3477.979957
pmid:18238101
fatcat:2dfpi7xa6zc63fzrqfwzopgsvi
*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. ...##
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Decision diagrams in machine learning: an empirical study on real-life credit-risk data

2004
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Expert systems with applications
*

Alternatively,

doi:10.1016/j.eswa.2004.02.001
fatcat:kf46majsdvgd3g4kknk5udy3mi
*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. ...##
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Decision Diagrams in Machine Learning: An Empirical Study on Real-Life Credit-Risk Data
[chapter]

2004
*
Lecture Notes in Computer Science
*

Alternatively,

doi:10.1007/978-3-540-25931-2_49
fatcat:jteqm2iyj5gkvccnnsegryu5tu
*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. ...##
###
Ordered binary decision diagrams and minimal trellises

1999
*
IEEE transactions on computers
*

We would like to thank Randy Bryant for several helpful and informative discussions on binary

doi:10.1109/12.795225
fatcat:72as4nzt7bbifhbgtvlab3ertu
*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. ...
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