On the representational power of bit-level and word-level decision diagrams

Becker, Bernd; Drechsler, Rolf; Enders, Reinhard

doi:10.1109/aspdac.1997.600304

Cited by 20 publications

(8 citation statements)

References 15 publications

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“…Using *BMDs it was for the first time possible to verify multipliers of bit length up to n=256, however, they fail for the representation of Boolean functions that can easily be represented using BDDs. A thorough review of different Decision Diagrams can be found in [14]. They still suffer from memory explosion when dealing with wide arithmetic operations due to defining functions over binary variables as a bit vector rather than integer variables.…”

Section: Related Workmentioning

confidence: 99%

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Modular equivalence verification of polynomial datapaths with multiple word-length operands

Alizadeh

Fujita

2011

2011 IEEE International High Level Design Validation and Test Workshop

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In this paper, we extend Modular Horner Expansion Diagram (Modular-HED) as a canonical polynomial representation to verify polynomial functions with multiple bit-width operands from nd n n Z Z Z 2 2 2 ... 2 1 × × to n Z 2 . Our contributions are mostly in efficient implementation of [1] with a canonical decision diagram in such a way that both verification and synthesis of large arithmetic circuits can be more efficient. The experimental results show the effectiveness of our approach in comparison with other decision diagrams and algebraic techniques.

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Section: Related Workmentioning

confidence: 99%

“…then the leading term is reduced to LC*(LM-(lines[13][14]. If, however, ∀i=1,…,d: k i < µ i , then the reduction is performed based onLemma 1 and Theorem 2.…”

mentioning

confidence: 99%

Modular equivalence verification of polynomial datapaths with multiple word-length operands

Alizadeh

Fujita

2011

2011 IEEE International High Level Design Validation and Test Workshop

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“…In a first series of experiments we compare K*BMDs to other data structures, like EVBDDs [25], OFDDs [23] and *BMDs [10,11], on some of the clique functions for graphs from [20,4,3]:…”

Section: Variable Ordering and Decomposition Type Choicementioning

confidence: 99%

Manipulation algorithms for K*BMDs

Drechsler¹,

Becker²,

Ruppertz

1997

Tools and Algorithms for the Construction and Analysis of Systems

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Bit-level and word-level based Decision Diagrams (DDs) have led to significant advances in the area of Computer Aided Design (CAD). Recently, a new data structure for the word-level, called Kronecker Multiplicative BMDs (K~BMDs), has been presented. We study manipulation algorithms for K~BMDs: Using K~BMDs it is possible to represent functions efficiently, that have a good word-level description (like multipliers). On the the other hand K*BMDs are also applicable to verification problems at the bit-level. We clarify the relation between bit-and word-level representation which is of impo~'tance in particular in the context of verification. Experiments show that ~BMDs are not wellsuited for the bit-level. On the other hand OBDDs are not applicable on the word-level. We present algorithms that allow to dynamically switch between bit-level and word-level. We discuss a method for changing the decomposition type and variable order. First experiments demonstrate the efficiency of K*BMDs as a data structure that is suitable for bit-level and word-level functions as well, e.g. K~BMDs can e~ciently represent all of the LGSynth91, ISCAS85, and ISCASS9 benchmarks.

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“…It is known from [2]: The OFDD for a Boolean function represented by a *BMD can be obtained by performing a modulo 2 operation in each node and reducing the resulting graph.…”

Section: Preliminariesmentioning

confidence: 99%

Manipulation of *BMDs

Drechsler

Höreth

Proceedings of 1998 Asia and South Pacific Design Automation Conference

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Multiplicative Binary Moment Diagrams (*BMDs) have recently been introduced as a data structure for verification. Using *BMDs it was for the first time possible to verify multiplier circuits with up to 256 bits.In this paper we use a modification of *BMDs, called positive *BMDs (p*BMDs), that allows to apply dynamic variable ordering, that is the most promising minimization technique for decision diagrams, to *BMDs. Furthermore, we study *BMDs representing Boolean functions. We show that in this case for some operations polynomial algorithms can be given, while the general case of integer-valued functions requires exponential effort.Experimental results demonstrate that p*BMDs clearly outperform *BMDs with respect to runtime during dynamic minimization, while keeping (nearly) all advantages.

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On the representational power of bit-level and word-level decision diagrams

Cited by 20 publications

References 15 publications

Modular equivalence verification of polynomial datapaths with multiple word-length operands

Modular equivalence verification of polynomial datapaths with multiple word-length operands

Manipulation algorithms for K*BMDs

Manipulation of *BMDs

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