Team:MoWestern Davidson/project mathmodel

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Fine distributions look deeper at how each clause was satisfied, either singly or doubly. If an input satisfies one or two literals in a clause, that clause is satisfied singly or doubly respectively. Here is a example of fine distribution using the problem from the table above.  
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Fine distributions look deeper at how each clause was satisfied. If an input satisfies one or two literals in a clause, that clause is satisfied '''singly''' or '''doubly''' respectively. The fine distribution for the red problem from the table above is '''0011212100'''. This distribution means that 0 inputs satisfied 0 clauses, 0 inputs satisfied 1 clause singly, 1 input satisfied 1 clause doubly, 1 input satisfied 2 clauses with 2 singles, 2 inputs satisfied 2 clauses with 1 single and 1 double, 1 input satisfied 2 clauses with 2 doubles, 2 inputs satisfied 3 clauses with 3 singles, 1 input satisfied 3 clauses with 2 singles and 1 double, 0 inputs satisfied 3 clauses with 1 single and 2 doubles, and 0 inputs satisfied 3 clauses with 3 doubles.

Revision as of 16:28, 27 July 2009

Lego Models

B2 Bomber

Rough and Fine distribution

To classify SAT problems, we began looking at the Rough distribution of each problem, meaning how many inputs satisfied a certain number of clauses in a problem. The table below gives the number of clauses satisfied for a few select 2-SAT problems for each input.


Table2.png


Fine distributions look deeper at how each clause was satisfied. If an input satisfies one or two literals in a clause, that clause is satisfied singly or doubly respectively. The fine distribution for the red problem from the table above is 0011212100. This distribution means that 0 inputs satisfied 0 clauses, 0 inputs satisfied 1 clause singly, 1 input satisfied 1 clause doubly, 1 input satisfied 2 clauses with 2 singles, 2 inputs satisfied 2 clauses with 1 single and 1 double, 1 input satisfied 2 clauses with 2 doubles, 2 inputs satisfied 3 clauses with 3 singles, 1 input satisfied 3 clauses with 2 singles and 1 double, 0 inputs satisfied 3 clauses with 1 single and 2 doubles, and 0 inputs satisfied 3 clauses with 3 doubles.



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