Labeled rough partitions ¯ a new general purpose representation for multiple-valued functions and relations

In this paper, we present a new data structure for representing multiple-valued (MV) relations (functions in particular), both completely and incompletely specified, and an associated set of manipulation algorithms. Relations are represented by labeled rough partitions, structure similar to rough partitions introduced in [T. Luba, Decomposition of multiple-valued functions, in: Proceedings of the 25th ISMVL, 1995, pp. 256¯261] but extended with labels to store the full information about relations. We present experimental results from comparison of our data structure to binary decision diagrams (BDDs) on binary functions (MCNC benchmarks) showing its superiority in terms of memory requirements in 73% cases. The new representation can be used to a large class of MV, completely and incompletely specified functions and relations, typical for machine learning and complex finite state machine (FSM) controller optimization applications.