1. Inductively Finding a Reachable State Space Over-Approximation EE 290a Project Presentation Mike Case

2. 2 Sequential Optimization One optimization approach: State space Can be used as don’t cares Reachable state space Requires state reachability analysis  Prohibitively expensive  Can be approximated

3. Mike Case3 Van Eijk’s Method Uses induction rather than reachability analysis  Fast but incomplete Finds sequentially equivalent nodes in a network  Nodes are identical in every reachable state States where equivalences hold is an over-approximation of the reachable states

4. Mike Case4 Van Eijk’s Inductive Hypothesis Base Case:  A set of node equivalences holds for the initial state Inductive Hypothesis:  If equivalences hold in one state then they hold in every 1-reachable state as well

5. Mike Case5 Van Eijk Weaknesses Originally for equivalence checking Doesn’t find many sequential equivalences in optimization

6. Mike Case6 Generalizing Van Eijk Find implications rather than exact equivalences AB A  B 001 011 100 111 Implications subsume equivalences  (A  B)  (B  A)  (A = B)

7. Mike Case7 Implication Inductive Hypothesis Base Case:  A set of node implication holds for the initial state Inductive Hypothesis:  If implications hold in one state then they hold in every 1-reachable state as well Exactly like Van Eijk!

8. Mike Case8 State Reachability Induction gaurantees:  In every reachable state, implications hold State space States where implications hold Reachable state space

9. Mike Case9 Sequential-Only Implications Combinational implications:  True for every state  Tell us nothing Sequential implications:  True for every reachable state  Gives reachable state space approximation

10. Mike Case10 Implementation Overview Implemented in MVSIS Used and-inverter graphs and SAT

11. Mike Case11 Base Case = 1?

12. Mike Case12 Inductive Step

13. Mike Case13 Results - Performance

14. Mike Case14 Results – State Space DCs

15. Mike Case15 Results - Synthesis