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Reduction of sizes of decision diagrams by autocorrelation functions,”
 IEEE Trans. on Computers,
, 2003
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Augmented Sifting of MultipleValued Decision Diagrams
, 2003
"... Discrete functions are now commonly represented by binary (BDD) and multiplevalued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of ..."
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Cited by 8 (3 self)
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Discrete functions are now commonly represented by binary (BDD) and multiplevalued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of BDD sifting where XOR operations involving adjacent variable pairs augment adjacent variable interchange leading to further reduction in the node count. In this paper, we consider the extension of this approach to MDDs. In particular, we show that the XOR operation of linear sifting can be extended to a variety of operations. We term the resulting approach augmented sifting. Experimental results are presented showing sifting and augmented sifting can be quite effective in reducing the size of MDDs for certain types of functions.
Variable Ordering for Taylor Expansion Diagrams
 in IEEE Intl. High Level Design Validation and Test Workshop
, 2004
"... Abstract: This paper presents an algorithm for variable ..."
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Cited by 5 (4 self)
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Abstract: This paper presents an algorithm for variable
Efficient manipulation algorithms for linearly transformed BDDs
 Proc. 4 th Int’l Workshop on Applications of ReedMuller Expansions
, 1999
"... Binary Decision Diagrams (BDDs) are the stateoftheart data structure in VLSI CAD. But due to their ordering restriction only exponential sized BDDs exist for many functions of practical relevance. Linear Transformations (LTs) have been proposed as a new concept to minimize the size of BDDs and it ..."
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Cited by 3 (0 self)
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Binary Decision Diagrams (BDDs) are the stateoftheart data structure in VLSI CAD. But due to their ordering restriction only exponential sized BDDs exist for many functions of practical relevance. Linear Transformations (LTs) have been proposed as a new concept to minimize the size of BDDs and it is known that in some cases even an exponential reduction can be obtained. In addition to a small representation, the efficient manipulation of a data structure is also important. In this paper we present polynomial time manipulation algorithms that can be used for Linearly Transformed BDDs (LTBDDs) analogously to BDDs. For some operations, like synthesis algorithms based on ITE, it turns out that the techniques known from BDDs can be directly transferred, while for other operations, like quantification and cofactor computation, completely different algorithms have to be used. Experimental results are given to show the efficiency of the approach. 1
Symbolic Representation with Ordered Function Templates
 DAC 2003
, 2003
"... Binary Decision Diagrams (BDDs) often fail to exploit sharing between Boolean functions that differ only in their support variables. In a memory circuit, for example, the functions for the different bits of a word differ only in the data bit while the address decoding part of the function is identic ..."
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Cited by 1 (0 self)
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Binary Decision Diagrams (BDDs) often fail to exploit sharing between Boolean functions that differ only in their support variables. In a memory circuit, for example, the functions for the different bits of a word differ only in the data bit while the address decoding part of the function is identical. We present a symbolic representation approach using ordered function templates to exploit such regularity. Templates specify
4. TITLE AND SUBTITLE Characteristics of the Binary Decision Diagrams of Boolean Bent Functions
, 2009
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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to
Lower Bounds for Linear Transformed OBDDs and FBDDs
"... Abstract: Linear Transformed Ordered Binary Decision Diagrams (LTOBDDs) have been suggested as a generalization of OBDDs for the representation and manipulation of Boolean functions. Instead of variables as in the case of OBDDs parities of variables may be tested at the nodes of an LTOBDD. By this e ..."
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Abstract: Linear Transformed Ordered Binary Decision Diagrams (LTOBDDs) have been suggested as a generalization of OBDDs for the representation and manipulation of Boolean functions. Instead of variables as in the case of OBDDs parities of variables may be tested at the nodes of an LTOBDD. By this extension it is possible to represent functions in polynomial size that do not have polynomial size OBDDs, e.g., the characteristic functions of linear codes. In this paper lower bound methods for LTOBDDs and some generalizations of LTOBDDs are presented and applied to explicitly defined functions. By the lower bound results it is possible to compare the set of functions with polynomial size LTOBDDs and their generalizations with the set of functions with polynomial size representations for many other restrictions of BDDs.
Use of Gray Decoding for Implementation of Symmetric Functions
"... Abstract — This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity ReedMuller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation c ..."
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Abstract — This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity ReedMuller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation cost of symmetric functions based on these expressions by exploiting Gray decoding of input variables. Although this decoding is a particular example of all possible linear transformation of Boolean variables, it is efficient in the case of symmetric functions since it provides a significant simplification of SOPs and FPRMs. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method. Index Terms — Symmetric function, Gray code, linear transformation, autocorrelation.
systems.com
"... Binary Decision Diagrams (BDDs) often fail to exploit sharing between Boolean functions that differ only in their support variables. In a memory circuit, for example, the functions for the different bits of a word differ only in the data bit while the address decoding part of the function is iden ..."
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Binary Decision Diagrams (BDDs) often fail to exploit sharing between Boolean functions that differ only in their support variables. In a memory circuit, for example, the functions for the different bits of a word differ only in the data bit while the address decoding part of the function is identical. We present a symbolic representation approach using ordered function templates to exploit such regularity. Templates specify functionality without being bound to a specific set of variables. Functions are obtained by instantiating templates with a list of variables. We ensure canonicity of the representation by requiring that templates are normalized and argument lists are ordered. We also present algorithms for performing Boolean operations using this representation. Experiments with a prototype implementation built on top of CUDD indicate that function templates can dramatically reduce memory requirements for symbolic simulation of regular circuits.