Multi-Level Logic Synthesis

Summary

In this chapter we have examined how both algebraic and Boolean factored forms can be used to compactly represent multilevel logic. The algebraic methods discussed are anomalous in the sense that they do not obey the laws of Boolean algebra of Chapter 3. Along the way, we have characterized Syntactically equivalent, maximally factored, and optimum factored forms.

We have presented the ideas and given illustrative examples for the elegant theory of kernels and co-kernels of [38], as expressed in Theorem 10.5.1 of Page 426. We have shown how kernels and co-kernels can be computed and used to root out any and all common subexpressions in the algebraic subexpressions implicitly present in two-level or multilevel logic. Methods have been given for computing all or part of the sets of kernels and co-kernels.

We have presented in detail the “recursive generic factoring” approach, which is the key idea in the SIS suite of algebraic synthesis tools. We have shown how the idea of “weak (algebraic) division” plays a key role in this approach, and have given many examples and problems which demonstrate and motivate these concepts.