1. SINGLE-LEVEL PARTITIONING SUPPORT IN BOOM-II
Petr Fišer, Hana Kubátová
Department of Computer Science and Engineering
Czech Technical University

2. Outline Motivation Single-Level Partitioning
Constraint-Driven Minimization
BOOM-II & Its Modifications
Experimental Results
Conclusions

3. Motivation
Typical logic synthesis process:
Perform two-level minimization
Then do the decomposition, independently on the previous phase
Then apply other criteria (low power, DFT) 
Two-level minimization is performed independently on the following phases – can misguide the solution

4. Single-Level Partitioning
Two-level AND-OR network
The issue: limited number of inputs/outputs in real devices
Solution: divide the circuit into stand-alone blocks, while reducing number of their inputs
In praxis, not all the inputs are needed to generate values of particular outputs  it is possible

5. Constraint-Driven Minimization
Two-level Partitioning - divide circuit into blocks - keep the number of inputs minimal
Design for Testability - reduce the cone size
Load Balancing - divide circuit into blocks - reduce the number of branchings
???

6. BOOM-II Heuristic two-level Boolean minimizer
Composition of two minimizers - BOOM - FC-Min
BOOM is suitable for functions with a large number of inputs
FC-Min is suitable for functions with a large number of outputs
Iterative minimization – both the minimizers are being alternated

7. BOOM-II

8. BOOM: CD-Search
Generates an irredundant set of implicants covering the on-set of a single-output function
Implicants are being constructed top-down, i.e., by reducing a universal hypercube until it becomes an implicant - by adding literals to a term
Greedy heuristic

9. BOOM: CD-Search
Literals to be added to a term are being selected using a scoring function - frequency of occurrence
For partitioning: the frequency of the literal that is already included in the processed block is multiplied by the CD-Search partitioning force

10. BOOM: IE, IR
Implicant Expansion - expands implicants to PIs - no modification
Implicant Reduction - reduces PIs to group implicants - no modification

11. FC-Min: Find Cover Generates a cover of the on-set
Determines the number of product terms in the solution, not their structure
It is not dependent on input literals – cannot be modified
However - it strictly defines what terms would be shared among what output variables - it determines what outputs would be grouped together

12. FC-Min: Implicant Generation
Generates implicants from the cover
Purely deterministic – cannot be modified

13. FC-Min: Implicant Expansion
Expands implicants to reduce no. of literals
Can be influenced - literals of variables included in other blocks are removed first

14. CP Solution The essential phase Finds an irredundant set of implicants
Constructs the final solution
A greedy incremental heuristic, based on a scoring function
To apply partitioning, additional weights are assigned to the implicants, the weights modify the scoring function

15. Experimental Results
Boolean function: 50 inputs, 40 outputs, into 4 blocks
no partitioning
with partitioning
Sum of # of inputs
200
114
Branchings
150 67
Maximum load 4
Average load
2.34
GEs
2375.5
2874.5
Block 0 inputs 50 30
Block 1 inputs
Block 2 inputs 26
Block 3 inputs 28

16. Conclusions
Constraint-Driven two-level minimization support in BOOM-II was presented
Partitioning
Design for testability
Low power design …