E2: A new logic model for MVL relations Original Research Article

A new logic model is presented in this paper for subsets of Rn × Rm known as n-input m-output r-valued multiple-valued logic (MVL) relations, where n, m >0 and r >1 are integers, and R = {0,1, … , r − 1} is an enumeration of the finite ordered set E = {e0, e1,…, er−1}. The model, called E2 systems (or shortly E2), represents an extension of an existing generalized cube representation for MVL relations called set functions. E2 systems consist of two components: logic implication (LI) systems, and logic equivalence (LE) systems. Some properties of the E2 systems are presented, and applying the model in cell-based combinatorial MVL circuit synthesis is discussed.