An Approach for Simplifying Switching Functions by Utilizing the Cover Table Representation
IEEE Transactions on Computers
On the Determination of the Maximum Compatibility Classes
IEEE Transactions on Computers
On the Determination of Irredundant Prime Closed Sets
IEEE Transactions on Computers
Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets
IEEE Transactions on Computers
Derivation of maximal compatibles using Boolean algebra
IBM Journal of Research and Development
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
Sequential Algorithm for the Determination of Maximum Compatibles
IEEE Transactions on Computers
On the Equivalence of Two Algorithms for Finding All Maximal Compatibles
IEEE Transactions on Computers
CIMMACS'07 Proceedings of the 6th WSEAS international conference on Computational intelligence, man-machine systems and cybernetics
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The compatibility relation occurs in many different disciplines in science and engineering. When a compatibility relation exists between pairs of elements in a set, an important problem is to derive the collection of aU those elements that form maximal compatibles. If the set of elements with the compatibility relation can be visualized as a compatibility graph of which the different nodes represent the elements of the set, the only edges of the graph being the nonoriented lines joining pairs of elements with the compatibility relation, then the problem of deriving the maximal compatibles becomes identical to the graph theory problem of finding all the maximal complete subgraphs in a symmetric graph. Recently, in connection with simplifying incompletely specified sequential machines, where a kind of compatibility relation also exists between pairs of internal states, Das and Sheng proposed a method for deriving the different maximal compatibles through finding all of the modified cut-sets of the incompatibility graph of the machine. This paper, without confining itself to only incompletely specified machines, considers the problem involving the compatibility relation in a broader perspective and suggests a new approach for finding aU the modified cut-sets of the incompatibility graph of a set having a compatibility relation between its different pairs of elements.