Grygiel, S., Perkowski, M., MarekSadowska, M., Luba, T., and Jozwiak, L. (1997). Cube diagram bundles: a new representation of strongly unspecified multiple-valued functions and relations. In Proc. of ISMVL'97, pages 287--292, Halifax, Nova Scotia, Canada.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....10001110 01 11111110 11 10110011 10 10110011 Fig. 11. The Karnaugh map for MVR F(A,B) a 0 1 b 2 b 2 b 1 b 1 v 2 v 1 v 2 v 2 v 2 Fig. 12. The BEMDD for MVR F(A,B) 10 Labeled Rough Partitions Recently, Labeled Rough Partitions (LRPs) have been introduced as a new representation of MVRs [31,32]. This representation is similar to BEMDDs in that it relies on encoding and characteristic functions. It is different from BEMDD representation in that the cube table specifying the MVR is read and encoded vertically, column by column, rather than horizontally, line by line. Given the cube table ....

S.Grygiel, M.Perkowski, M.Marek-Sadowska, T.Luba, L.Jozwiak. "Cube Diagram Bundles: A New Representation of Strongly Unspecified Multi-Valued Functions and Relations". Proc. of ISMVL'97, Halifax, Nova Scotia, Canada, May 1997, pp. 287-292.

....Manuscript completed June 26, 1997. blankets for certain types of generalized set systems [3] For a discussion of other works related to Boolean function decomposition and its applications see [3] Decompositions of multiple valued functions and relations have been studied recently in [5, 7, 9]; for a discussion of the literature in this field we refer the reader to these papers. In [7] rough partitions (blankets) are used to represent functions. The authors of [5, 9] use generalized don t cares, i.e. situations in which an output may take on any value in some set that is a proper ....

....its applications see [3] Decompositions of multiple valued functions and relations have been studied recently in [5, 7, 9] for a discussion of the literature in this field we refer the reader to these papers. In [7] rough partitions (blankets) are used to represent functions. The authors of [5, 9] use generalized don t cares, i.e. situations in which an output may take on any value in some set that is a proper subset of the domain of that output. For example, for a domain of f0; 1; 2g, an output may be allowed to take the values 0 or 2, but not 1. The present paper extends the work in ....

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S. Grygiel, M. Perkowski, M. Marek-Sadowska, T. / Luba, and L. J'o'zwiak, Cube Diagram Bundles: A New Representation of Strongly Unspecified Multiple-Valued Functions and Relations, Proc. IEEE International Symposium on Multiple-Valued Logic, Antigonish, Nova Scotia, Canada, pp. 287--292, May 1997.

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Grygiel, S., Perkowski, M., MarekSadowska, M., Luba, T., and Jozwiak, L. (1997). Cube diagram bundles: a new representation of strongly unspecified multiple-valued functions and relations. In Proc. of ISMVL'97, pages 287--292, Halifax, Nova Scotia, Canada.

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S. Grygiel, M. Perkowski, M. Marek-Sadowska, T. Luba, L. Jozwiak, "Cube Diagram Bundles: A New Representation of Strongly Unspecified Multiple-Valued Functions and Relations," Proc. ISMVL'97, pp. 287-292.

....5 inputs, and the increased computation time required for partitioning, column compatibility checking, column minimization and encoding when bound sets are large. Previously, column compatibility checking was performed in a pairwise fashion referred to here as the Pair Compatibility Approach(PCA) [7, 8, 12, 10, 4]. The basic idea behind the PCA is to check the compatibility relationship of each column with every other column one pair at a time. The new approach presented in this paper is referred to as the Group Compatibility Approach(GCA) The basic idea behind the GCA is to check the compatibility ....

....bound sets create on average more overlaps when multi coloring is used instead of coloring of the incompatibility graphs. Thus, as demonstrated in [9] they lead more often to decomposition of both blocks G and H of the decomposition being relations, when the relational decomposition is applied [10, 4]. In addition to saving time when the bound sets are large, this new approach can be used to search a significant part of the search space on large functions not feasible using previous approaches due to the large computational requirements. The new approach can be integrated into a modified graph ....

S. Grygiel, M. Perkowski, M. Marek-Sadowska, T. Luba, and L. Jozwiak, "Cube Diagram Bundles: A New Representation of Strongly Unspecified Multiple-Valued Functions and Relations," Proc. ISMVL '97, pp. 287-292.

.... approaches of modern logic synthesis is general functional decomposition [17, 20, 11] Together with our collaborators, we developed decomposers TRADE [27] LUTSYN [26] and GUD (all binary) FRED [11, 12] multi valued functions) and finally GUD MV lued) for multivalued functions and relations [20, 13, 14]. Observe, that unlikely to TRADE that uses cubes and FRED and most recent decomposers that use BDDs (Pedram et al., Scholl [23] Wurth et al.) GUD and GUD MV use a new data structure, based on BDD encoded or bit set encoded labeled rough partitions [13, 14] Karnaugh maps are used below only for ....

.... multivalued functions and relations [20, 13, 14] Observe, that unlikely to TRADE that uses cubes and FRED and most recent decomposers that use BDDs (Pedram et al., Scholl [23] Wurth et al.) GUD and GUD MV use a new data structure, based on BDD encoded or bit set encoded labeled rough partitions [13, 14] (Karnaugh maps are used below only for easier explanation) This new data structure allows to realize algorithms tuned to multi valued relations and don t cares, which would be difficult to implement in BDD based approaches. Don t cares have many interesting applications in decomposition, ....

[Article contains additional citation context not shown here]

S. Grygiel, M. Perkowski, M. Marek-Sadowska, T. Luba, and L. Jozwiak, "Cube Diagram Bundles: A New Representation of Strongly Unspecified Multiple-Valued Functions and Relations," Proc. ISMVL'97, Canada.

....same color. This is called Clique Covering. If the graph is represented as an Incompatibility Graph then nodes which do not have a common edge can be colored with the same color. This is called Graph Coloring. It was shown to be efficient, especially for functions with high percent of don t cares [4,9,10,11] Although few authors studied graph coloring in Functional Decomposition, nobody, to our knowledge, has compared these methods, or evaluated the importance of finding minimal solutions to the problem of Column Multiplicity in the Ashenhurst Curtis Decomposition. In this paper we will compare two ....

....is 1. 2] Now select a new GNODE which is node B . GNODE B can be given the possible colors 2; 3; 4; 5; 6. Store this information on SNODE labeled SNODE 2 in Fig. 2. Selected color is 2. 3] Now GNODE C becomes the selected node and it can obtain one of colors f3,4,5,6g. Selected color is 3. [4] In this way, the first branch of the tree from Fig. 2 is created. After finding the first solution: color 1 = fAg, color 2 = fB,D,Eg, color 3 = fCg. we know that three colors are enough, and these colors are 1, 2 and 3. 5] All non used colors are then removed from sets POSS of all previous ....

[Article contains additional citation context not shown here]

S. Grygiel, M. Perkowski, M. Marek-Sadowska, T. Luba, L. Jozwiak, "Cube Diagram Bundles: A New Representation of Strongly Unspecified Multiple-Valued Functions and Relations," Proc. ISMVL'97.

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