UCR CS220, Fall 2000, Prof. Frank Vahid
Homework 3, due Tuesday 12/5/00 at the beginning of lecture


1. Use the tabulation (Quine-McCluskey) method to minimize the 
   function F(w,x,y,z) = SUM(1,4,6,7,8,9,10,11,15).

2. (a) Define your own script for heuristic two-level logic minimization,
   consisting of 5 steps, each step being one of the basic operators 
   expand, reduce, reshape, and irredundant. For simplicity, do not
   include a loop in your script. (b) Then, apply your script
   to the original (unminimized) function F above, showing the results
   after each step, and the final results. Your script should provide
   some improvement for this example. 

3. (a) Devise a simple greedy heuristic for multi-level logic minimization, 
   using no more than three basic operators in the book. The cost function 
   should be the total number of gate inputs; numbers of gates themselves or 
   number of levels does not matter. (b) Apply your greedy heuristic to the 
   original F above.  Your heuristic should be such that it provides some
   improvement for this example. (c) Manually try to find the optimal 
   multi-level solution (don't go overboard, just try for a while), and 
   compare the results with your heuristic.

4. Create an instance of a minimum-cutsize graph partitioning problem,
   such that a greedy heuristic won't find the optimum solution, but
   the group migration heuristic would. Your graph should have exactly
   6 vertices.  Any partitions that have between 2 and 4 nodes in a part
   are acceptable. You can assign any initial partitioning as input to
   Trace the greedy and group migration heuristics on this initial
   partitioning, showing the intermediate steps and final results.