U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," in Proc. European Design and Test Conference, pp. 43--47, Paris, France, March 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....size and shape with respect to the variable ordering chosen, etc . motivate an increasing research activity in this area. Research directions include in particular: Ef Thetacient implementations [8, 9] development of ordering heuristics [10, 11, 12] and alternative representations altogether [13, 14, 15, 16, 17]. In [18] the authors presented an addition to the basic ROBDD representation, based on the analogy of ROBDDs with deterministic Thetanite automata. The new representation was a counterpart of a nondeterministic automaton (hence possibly more compact) in which a function rooted at each ROBDD ....

U. Kebschull, E. Schubert, and W. Rosentiel. Multilevel logic based on functional decision diagrams. In EuroDAC, Proceedings of the European Conference on Design Automation, pages 43#47, September 1992.

....of a linear function in terms of its moments, and they have weights associated with their edges which are combined multiplicatively. These features have as heritage ideas found in previous function representations, namely the Reed Muller decomposition used by Functional Decision Diagrams (FDDs) [9, 14], and the additive edge weights found in Edge Valued Binary Decision Diagrams (EVBDDs) 15] The relations between the various representations are described more fully below. BMDs are particularly effective for representing digital systems at the word level, where sets of binary signals are ....

....to the ReedMuller expansion (also called the positive Davio expansion [9] for Boolean functions: f = f x Phi x (f x Phi f x ) The expression f x Phif x is referred to as the Boolean difference of f with respect to x [21] and in many ways is analogous to our linear moment. Other researchers [9, 14] have explored the use of graphs for Boolean functions based on this expansion, calling them Functional Decision Diagrams (FDDs) By our terminology, we would refer to such a graph as a moment diagram rather than a decision diagram. 2.2. Edge Versus Terminal Weights 0 1 x 0 2 x 1 4 x 2 0 1 x ....

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U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," European Design Automation Conference, 1992, pp. 43--47.

.... This is the reason why many authors investigate the usefulness of generalizations or modifications of OBDDs for design automation (see e.g. GM92, SW92a, LS92] In this context a new type of decision diagram, called ordered functional decision diagram (OFDD) has recently been introduced ( KSR92, KR93, BDT93] BDDs (FDDs) are directed acyclic graphs, where a Shannon decomposition (Reed Muller decomposition) is carried out in each node. While BDDs naturally correspond to AND OR multi level logic circuits and in this sense are suitable for synthesis tools that target on circuits realized ....

.... AND EXOR realizations proved to be very efficient for large classes of circuits, e.g. arithmetic circuits, error correcting circuits and circuits for tele communication ( Ber68, Sau92] and, in addition, have nice testability properties ( Red72, DB93] First experimental results given in [KSR92, SKR92, KR93, BDT93] demonstrate that OFDDs might be very useful for AND EXOR based synthesis and might even be an interesting alternative data structure for the representation of Boolean functions. Up to now a theoretical background for OFDDs as it exists for OBDDs with the huge number of ....

[Article contains additional citation context not shown here]

U. Kebschull, E. Schubert, and W. Rosenstiel. Multilevel logic based on functional decision diagrams. In Proceedings of EDAC'92, pages 43--47, 1992.

....of a linear function in terms of its moments, and they have weights associated with their edges which are combined multiplicatively. These features have as heritage ideas found in previous function representations, namely the Reed Muller decompositionused by Functional Decision Diagrams (FDDs) [8], and the additive edge This research is sponsoredby the Wright Laboratory,AeronauticalSystems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F33615 93 1 1330. 0 This paper will appear in the 32nd Design Automation Conference, June ....

....moment decomposition of Equation 2 is analogousto the ReedMuller expansion for Boolean functions: f = f x Phi x (fx Phi f x ) The expression fx Phi f x is commonly known as the Boolean difference of f with respect to x, and in many ways is analogous to our linear moment. Other researchers [8] have explored the use of graphs for Boolean functions based on this expansion, calling them Functional Decision Diagrams (FDDs) By our terminology, we would refer to such a graph as a moment diagram rather than a decision diagram. 2.2. Edge Weights The BMD data structure encodes numeric ....

U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," European Design Automation Conference, 1992, pp. 43--47.

....x. The first equality in (10) is known as either the Reed Muller or the negative Davio expansion, while the second equality is referred to as the positive Davio expansion. These decompositions are analogous to the Taylor expansion of a differentiable function. The Reed Muller expansion can be used [46] as the basis for graphical representations called ordered functional decision diagrams. This representation is analogous to OBDDs, except that the outgoing edges from a vertex represent the negative cofactor and Boolean difference of the function with respect to the vertex variable. Ordered ....

U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," in Proc. European Design and Test Conference, pp. 43--47, Paris, France, March 1992.

....acceptance in VLSI, formal verification, and other fields. Subsequently, several researchers have generated a menagerie of BDD variants that relax, modify, or extend the rules governing the construction of BDDs, e.g. if then else DAG [54] MDD [83, 53] XBDD [50] snDD [49] EVBDD [57] FDD [55], SQBDD [70, 69] OPDD [74] ADD [1] etc. to name only a few. Accordingly, when there is risk of confusion in the literature, the BDD described here is dubbed an ROBDD, for reduced (because the reduction rules were applied) ordered (because the variables are always in the same order from root to ....

U. Kebschull, E. Schubert, and W. Rosenstiel. Multilevel logic based on functional decision diagrams. In European Conference on Design Automation (EDAC), pages 43--47, 1992.

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U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," in Proc. European Design and Test Conference, pp. 43--47, Paris, France, March 1992.

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U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," European Design Automation Conference, 1992, pp. 43--47.

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U. Kebschull, E. Schubert, and W. Rosentiel, "Multilevel logic based on functional decision diagrams," European Design Automation Conference, 1992, pp. 43--47. 36

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