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Inductively Finding a Reachable State Space Over-Approximation

Inductively Finding a Reachable State Space Over-Approximation. EE 290a Project Presentation Mike Case. Sequential Optimization. One optimization approach:. State space. Reachable state space. Can be used as don’t cares. Requires state reachability analysis Prohibitively expensive

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Inductively Finding a Reachable State Space Over-Approximation

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

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

  3. 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 Mike Case

  4. 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 Mike Case

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

  6. Generalizing Van Eijk • Find implications rather than exact equivalences • Implications subsume equivalences • (A  B)  (B  A)  (A = B) Mike Case

  7. 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! Mike Case

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

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

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

  11. = 1? Base Case Mike Case

  12. InductiveStep Mike Case

  13. Results - Performance Mike Case

  14. Results – State Space DCs Mike Case

  15. Results - Synthesis Mike Case

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