Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Edge-valued binary decision diagrams for multi-level hierarchical verification
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
Spectral transforms for large boolean functions with applications to technology mapping
DAC '93 Proceedings of the 30th international Design Automation Conference
DAC '94 Proceedings of the 31st annual Design Automation Conference
Verification of arithmetic circuits with binary moment diagrams
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Binary decision diagrams and beyond: enabling technologies for formal verification
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
PHDD: an efficient graph representation for floating point circuit verification
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Word-level decision diagrams, WLCDs and division
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
On the Descriptive and Algorithmic Power of Parity Ordered Binary Decision Diagrams
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
On the Limitations of Ordered Representations of Functions
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
K*BMDs: A New Data Structure for Verification
EDTC '96 Proceedings of the 1996 European conference on Design and Test
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Several types of Decision Diagrams (DDs) have been proposed for the verification of Integrated Circuits. Recently, word-level DDs like BMDs, *BMDs, HDDs, K*BMDs and *PHDDs have been attracting more and more interest, e.g., by using *BMDs and *PHDDs it was for the first time possible to formally verify integer multipliers and floating point multipliers of “significant” bitlengths, respectively.On the other hand, it has been unknown, whether division, the operation inverse to multiplication, can be efficiently represented by some type of word-level DDs. In this paper we show that the representational power of any word-level DD is too weak to efficiently represent integer division. Thus, neither a clever choice of the variable ordering, the decomposition type or the edge weights, can lead to a polynomial DD size for division.For the proof we introduce Word-Level Linear Combination Diagrams (WLCDs), a DD, which may be viewed as a “generic” word-level DD. We derive an exponential lower bound on the WLCD representation size for integer dividers and show how this bound transfers to all other word-level DDs.