New compact representation of multiple-valued functions, relations, and non-deterministic state machines

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.