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An improved to ak max sat (max-sat problem)

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An improved to ak max sat (max-sat problem)

  1. 1. By: Mohammad Khosravi , Reza Ramezani To: Dr Moosavi 1 Electronic & Computer Department Isfahan University Of Technology
  2. 2.  Input: given a list of clauses C1, . . . ,Cm  Output: the maximum number of clauses which satisfied.  Unit Propagation (UP) algorithm use for compute LB when we have at least one unit clause, otherwise we will use Failed literal detection. 2
  3. 3.  Let 1 be the Max-SAT instance {x1, x2, x3,¬x1 x4,¬x1 x5,¬x4 ¬x5,¬x1 ¬x2 ¬x3, x1 ¬x2} Q = [x1, x2, x3]  x1 propagate { x2, x3, x4, x5,¬x4 ¬x5, ¬x2 ¬x3} Q = [x2,x3,x4,x5]  x2 propagate {x3, x4, x5,¬x4 ¬x5,¬x3} Q =[x3, x4, x5,¬x3] 3
  4. 4.  x3 propagate {#,x4, x5,¬x4 ¬x5} Inconsistent subformula detected by UP is {x1, x2, x3,¬x1 ¬x2 ¬x3} The remaining clauses {¬x1 x4,¬x1 x5,¬x4 ¬x5, x1 ¬x2} 4
  5. 5. {x1, x2, x3,¬x1 x4,¬x1 x5,¬x4 ¬x5,¬x1 ¬x2 ¬x3, x1 ¬x2} Q1 = [x1, x2, x3]  x1 propagate Q1 = [ x2, x3] { x2, x3, x4, x5,¬x4 ¬x5, ¬x2 ¬x3} Q2 = [x4, x5]  x4 propagate Q2 = [x5,¬x5]  x5 propagate 5
  6. 6.  Inconsistent subformula : {x1,¬x1 x4,¬x1 x5,¬x4 ¬x5}  remaining clauses: {x2, x3,¬x1 ¬x2 ¬x3, x1 ¬x2} Q1 = [x2, x3]  x2 propagate {x3,¬x1 ¬x3, x1 } Q1 = [x3] Q2 = [x1]  x1 propagate 6
  7. 7. {x3, ¬x3 } Q2 = [¬x3 ]  inconsistent subformula : {x2, x3,¬x1 ¬x2 ¬x3, x1 ¬x2}. 7
  8. 8. P={#,#, y ¬x,¬y z,¬y ¬z, y x}  P U {x},with UP  inconsistent subformula 1 = {x, y ¬x,¬y z,¬y ¬z}, P U {¬ x}, with UP inconsistent  Subformula 2= {¬x,¬y z,¬y ¬z, y x}  Final incosistant subformula=(1 U 2) {x,¬x} = {y ¬x,¬y z,¬y ¬z, y x}  We can use FL whit UP & UP* 8
  9. 9. Solutions for solving maxsat efficiency: Rules Unit Propagation Failed Literal Detection Selecting variables for propagation Data Structure 9
  10. 10. Each variable order computed from:  Binary-Length with two value.  Unit-Length with one value.  Total-Length that contain the number of clauses that variable occurs.  W(i) is sum of all above weights.  This weight will calculate for Var(i) and Var(-i).  Final Variable’s weight is W(i) + W(-i)  Each Variable with higher weight with select earlier for propagation 10
  11. 11. Each variable order computed from:  Binary-Length with three value.  Unit-Length with two value.  Third-Length with one value.  Total-Length that contain the number of clauses that variable occurs. AKMax-Sat solver ReCompute this weights at each level, such as: propagate variable, remove variable and restore variable. 11

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