1. Alan Mishchenko Robert Brayton UC Berkeley
Don’t-Care-Based Logic Restructuring with Unreachable-State Information
Alan Mishchenko Robert Brayton
UC Berkeley

2. Overview Introduction Parts and pieces Summary Sources of don’t-cares
Ways of capturing don’t-care information
Restructuring multi-level networks with don’t-cares
Summary

3. Introduction There can be a lot of unreachable states
They can be used for logic simplification/restructuring
Previous methods may be limited
Will try to develop a more general method
Will use modern implementation technologies
Induction to prove sequential properties
Implemented using SAT
Multi-level logic restructuring
Implemented using truth tables

4. Ways of Capturing Don’t-Cares
Sequential properties
One-hotness conditions
Clauses in terms of current-state variables
4-input clauses in terms of internal variables
etc
Should be proved inductively
Refinement iteration with speculative reduction

5. Restructuring with Don’t-Cares
Method 1 (pre-computation of EXDCs)
Prove inductive invariants (e.g. implications in terms of current-state variables)
Use them as external don’t-cares (EXDCs)
Image EXDCs into local spaces using windowing
Restructure multi-level logic using local don’t-cares
Method 2 (in-place computation of local DCs)
Use simulation to formulate desirable local properties (e.g. constraints on inputs of local cones)
Prove these properties inductively
Method 3 (proving target replacements)
Use simulation to come up with desirable replacements (e.g. area-reducing decompositions)
Prove these replacements inductively and use them
No need to compute don’t-cares explicitly

6. Multi-Level Network Optimization
Bi-decomposition algorithm
Group variables
Check decomposition feasibility
Compute functions after decomposition
Apply decomposition recursively
Comments
Works with don’t-cares
Efficiently propagates internal don’t-cares
Allows for on-the-fly resubstitution
Increases logic sharing
Can be implemented with truth tables
Very fast for functions up to 16 inputs XB XA XC F A B

7. Summary This is an early work Outlined several promising ideas
Need better understanding of how to use don’t-cares
Implementation will follow somewhere down the line