Finding the minimum column multiplicity for a bound set of variables is an important problem in Curtis decomposi-tion. To investigate this problem, we compared two graph-coloring programs: one exact, and another one based on heuristics which can give, however, provably exact results on some types of graphs. These programs were incorporated into the multi-valued decomposer MVGUD. We proved that the exact graph coloring is not necessary for high-quality functional decomposers. Thus we improved by orders of magnitude the speed of the column multiplicity problem, with very little or no sacrifice of decomposition quality. Comparison of our experimental results with competing de-composers shows that for nearly all benchmarks our solu-tions are best and time is usually not too high.

In this paper we present a new data structure for representing multiple-valued relations (functions in particular) both completely and incompletely specified. The same format can be used for non-deterministic state machines (deterministic in particular). Relations are represented by labeled rough partitions, a structure similar to rough partitions, but storing the full information about relations and allowing for dynamic optimization of both memory requirements and processing time. 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 multiple-valued, completely and incompletely specified functions and relations, typical for Machine Learning (ML) and complex FSM controller optimization applications.