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Decision Variable Ordering

Decision Variable Ordering. Target: Clauses A in refutation prove as more as possible. How about by changing the decision variable ordering? Decision early, resolution later? Goal Find out the relation between decision order and resolution order. Experiment Setup.

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Decision Variable Ordering

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  1. Decision Variable Ordering • Target: Clauses A in refutation prove as more as possible. • How about by changing the decision variable ordering? • Decision early, resolution later? • Goal • Find out the relation between decision order and resolution order.

  2. Experiment Setup • MiniSAT comparison between two cases • Case 1: Variable decision by original setting. • Case 2: Variable decision by increasing order. • Test Bench: uuf50-218 • Download from SATLIB – Benchmark Problems • http://www.cs.ubc.ca/~hoos/SATLIB/benchm.html • 50 variables, 218 clauses - 1000 instances, all unsat

  3. Experiment Results (1/2) *origi.: by original setting of MiniSAT. *incre.: by increasing order.

  4. Experiment Results (2/2) *origi.: by original setting of MiniSAT. *incre.: by increasing order.

  5. Refutation Proof (1/2) By original setting of MiniSAT

  6. Refutation Proof (2/2) By increasing order

  7. Discussion • In runtime • In small case • Don’t need variable ordering • In medium case • Seems good? • In large case • <10 mins becomes > 4 days • In refutation proof • Changes, but can’t figure out good or bad. • There is no regularity between variables and clauses in the general CNF formulas.

  8. Experiment Results • 10 test cases. • Ascending order v.s. MiniSAT • Plot variable ID and variable counts. 8

  9. Variable Counts (1/10) *pink: by MiniSAT. *blue: by ascending order.

  10. Variable Counts (2/10) *pink: by MiniSAT. *blue: by ascending order.

  11. Variable Counts (3/10) *pink: by MiniSAT. *blue: by ascending order.

  12. Variable Counts (4/10) *pink: by MiniSAT. *blue: by ascending order.

  13. Variable Counts (5/10) *pink: by MiniSAT. *blue: by ascending order.

  14. Variable Counts (6/10) *pink: by MiniSAT. *blue: by ascending order.

  15. Variable Counts (7/10) *pink: by MiniSAT. *blue: by ascending order.

  16. Variable Counts (8/10) *pink: by MiniSAT. *blue: by ascending order.

  17. Variable Counts (9/10) *pink: by MiniSAT. *blue: by ascending order.

  18. Variable Counts (10/10) *pink: by MiniSAT. *blue: by ascending order.

  19. Discussion Variable counts Ascending : MiniSAT = 2.43 : 1 MiniSAT heap order? Relation between resolution order and variable decision order. 19

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