Logic Synthesis

-Basic Concepts and Tools

Tao Lin Ohio Universtiy

February 17, 1998

Introductory to some basic concepts; Espresso; Brief description to the BDD (Binary

Decision Diagram).

Foundation for: combinational and sequential synthesis testing timing and false paths formal verication asynchronous synthesis automata theory optimal clocking schemes hazard analysis power estimation general combinatorics.

if f 1 = B n , f is the tautology, i.e. f1; if f 0 = B n , (f 1 =) f is not satisfiable; if f(x) = g(x) for all x B n , then f and g are equivalent; x 1 ; x 2 ; … are variables; x 1 ; x 1 ; x 2 ; x 2 ; … are literals;

A cover is prime irredundant if all itscubes are prime (irredundant).

A prime of f is essential (essential prime) if there is a min-term (essential vertex) in thatprime but in no other prime.

Shannon (Boole) Cofactors

Binary Recursion Tree

Unate Functions and Unate Covers

A function is unate in xi if it is either positiveunate or negative unate in xi .

Unate covers F have many extraordinary properties: If a cover F is minimal with respect to singlecube containment, all of its cubes are essential primes. In this case F is the unique minimum cube repre- sentation of its logic function. A unate cover represents the tautology iff it contains a cube with no literals, i.e. a single tautologous cube.

IRREDUNDANT

EXPAND

Main idea of EXPAND

REDUCE

Reduce is order dependent.

REDUCE Algorithm

Unate Algorithm for SCCC

LSTGASP

A Brief Description of BDD (Binary Decision Diagram)

Acknowledgement

Most of the materials used here were selected from EE219b course note of UC-Berkeley. The author of these notes is Mr. R.K.Brayton.

Many thanks to people who give me help on preparing this talk.