Applications and algorithms for solving satisfiability problems
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An introductory survey of applications and algorithms for the satisfiability problem
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Applications and algorithms for solving satisfiability problems
- 1. Satisfiability: Applications and Algorithms Jim Kukula [email_address]
- 5. Composing Functions a b b c
- 8. Decision Tree a b b c c c c 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1
- 9. Pruning Unnecessary Nodes a b b c c 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1
- 10. Reusing Duplicate Nodes a b b c 1 1 0 0 0 0 0 0 1 1 1 1 Tree becomes Diagram , or BDD
- 18. Dimacs Format p cnf 59056 323700 1 2 0 1 3 0 1 4 0 1 -5 0 1 6 0 1 -7 0 1 -8 0 1 -9 0 1 -10 0 -2 -3 -4 5 -6 7 8 9 10 -1 0 -11 -12 -13 14 0 -14 11 0 -14 12 0 -14 13 0
- 19. Random CNF P(Sat) 1 0 # Clauses / # Variables 1 0 2 3 4 5 6 7 Limit for large #V Small #V
- 24. Stuck-at Fault Model Circuit as designed Circuit as manufactured Test generation: find a input bit vector that will produce different outputs in correct versus faulty circuits 1
- 25. Circuit-Based SAT 1 Can we find input assignments to drive the circuit output to 1?
- 26. Circuit-Based SAT 1 1 1 Inputs to AND must be 1 for output to be 1
- 27. Circuit-Based SAT 1 1 1 0 At least one input of NAND must be 0 for output to be 1, so we make a choice.
- 28. Circuit-Based SAT 1 1 1 1 0 1 Inputs to NAND must be 1 for output to be 0
- 29. Circuit-Based SAT 1 1 1 1 0 1 1 1 Inputs to AND must be 1 for output to be 1
- 30. Circuit-Based SAT 1 1 1 1 0 1 1 1 Conflict! need to backtrack and make different choices
- 33. CNF Decision & Implication Decide:
- 34. CNF Decision & Implication Decide: Imply:
- 35. CNF Decision & Implication Decide: Imply: Imply:
- 36. CNF Decision & Implication Decide: Imply: Imply: Imply:
- 37. CNF Decision & Implication Decide: Imply: Imply: Imply: Decide:
- 38. CNF Decision & Implication Decide: Imply: Imply: Imply: Decide: Imply:
- 39. Implication Graph Chains of implication linked by pairs of clauses with common variable but opposite signs: opportunities for resolution
- 40. Learned Clauses Cut in implication graph corresponds to learned clause derivable by resolution Look for small cuts – short clauses are tighter constraints