  Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving,
Petrick's method and McBoole's method have been devised to simplify Boolean
expressions in order to optimize hardware implementation of digital circuits.
However, the algorithmic implementations of these methods are hard-coded and
also their computation time is proportional to the number of minterms involved
in the expression. In this paper, we propose KarNet, where the ability of
Convolutional Neural Networks to model relationships between various cell
locations and values by capturing spatial dependencies is exploited to solve
Karnaugh maps. In order to do so, a Karnaugh map is represented as an image
signal, where each cell is considered as a pixel. Experimental results show
that the computation time of KarNet is independent of the number of minterms
and is of the order of one-hundredth to one-tenth that of the rule-based
methods. KarNet being a learned system is found to achieve nearly a hundred
percent accuracy, precision, and recall. We train KarNet to solve four variable
Karnaugh maps and also show that a similar method can be applied on Karnaugh
maps with more variables. Finally, we show a way to build a fully accurate and
computationally fast system using KarNet.
