Bounded Sequential Equivalence Checking with Range-Equivalent Circuit, Node Merging, and NAR

1. Bounded Sequential Equivalence Checking with Range-Equivalent Circuit, Node Merging, and NAR Speaker: Wei-An Ji Adviser: Chun-Yao Wang Date: 2013. 10. 21

2. Outline • Problem Formulation • Introduction • Range-equivalent circuit • Implementation • Analysis • Future Work

3. Problem Formulation • Given: • Two sequentialcircuits • A timeframe k • Derive: • Bounded sequential equivalence checking (BSEC) at timeframe koptimized by range-equivalent circuitreplacement, node merging, and NAR

4. Introduction pMiter s27 • Bounded: timeframe k • Typical BSEC • Unroll • Sequential → Combinational • Miter construction • SAT solver Resyn2(s27)

5. Range-equivalent circuit • Range-equivalent circuit • Circuit of timeframe 0 to k-1 replacement

6. Implementation(1) original method: PPI’s range is what we care! our method: We don’t-carePO’s range!

7. Implementation(2) Add new PO Add new PI • In Chih Chung’s work, when we apply range function we ignore the new PI. • The circuit size has only 1% reduction. • In my work, I apply full range function. • The circuit size can have over 30% reduction. • Range’s over-approximation problem Remove old PO

8. Implementation(3)

9. Analysis(1) • Replace a tree structure with a PI. • Ex: a is PI, b, c are PPI POs a PIs O1 b O2 d c a O1 O2 d Result: If d’s function is b|c the replacement will over-approximate the output’s range.

10. Analysis(2) • When state set Sk doesn’t increase and result of BSEC with bounded value k is UNSAT, we can claim these two sequential circuit are equivalent. … -1 Range’s over-approximation makes the redundant range appear in -1set.

11. Analysis(3) • Replace a tree structure with a PI. • only replace PPI • replace PI and PPI a a O1 O1 PI , Range b O2 O2 d d c a O1 O1 d PI ? , Range b O2 O2 d c c

12. Analysis(4) • Replace a tree structure with a PI. C. only replace PI a O1 O1 d PI , Range b O2 O2 d c c

13. Analysis(5) • Merge two PI to reduce PI number, but don’t affect output’s range Ex: a, b, and c are PIs

14. Analysis(6) A: a and c are PPIs, bare PIs (PIreplace PPI ) result: PI

15. Analysis(7) B: a is PI, b and c are PPIs (PPIreplace PI ) result: PI

16. Analysis(8) C: c is PI, a and b are PPIs (PPIreplace PPI ) result: PI

17. Analysis(9) • When can we apply mergePI to circuit? • The reachable state must make the original output range same as new output range. • But we don’t maintain the reachable state. • Just handle the case that PI replaces PPI.

18. Analysis(10) • We add more PI to circuit, so the range function may spend more time. • PI# plays an important role in SAT solverand range function. • We can skip the cases that PI# is not decrease to make the range function run faster.

19. Future work(1) • Solve range’s over-approximation • Add some constrain in range function to make the circuit has correct range set but the circuit size is still decrease. • The circuit still has range’s over-approximation problem, but we should ignore the redundant range set. • Make range function run faster

20. Future work(2) • 老師生日快樂! • x • 我下次會認真寫作業。 • 林振宇不要再翹課了。