Don't cares and multi-valued logic network minimization

TLDR: This work addresses optimizing multi-valued (MV) logic functions in a multi-level combinational logic network and gives a recursive image computation to transform the don't cares into the space of local inputs of the node to be minimized.

Abstract: We address optimizing multi-valued (MV) logic functions in a multi-level combinational logic network. Each node in the network, called an MV-node, has multi-valued inputs and single multi-valued output. The notion of don't cares used in binary logic is generalized to multi-valued logic. It contains two types of flexibility: incomplete specification and non-determinism. We generalize the computation of observability don't cares for a multi-valued function node. Methods are given to compute (a) the maximum set of observability don't cares, and (b) the compatible set of observability don't cares for each MV-node. We give a recursive image computation to transform the don't cares into the space of local inputs of the node to be minimized. The methods are applied to some experimental multi-valued networks, and demonstrate reduction in the size of the tables that represent multi-valued logic functions.