Random formulae, logic E

June 1999


Sets of 3CNF(E) formulas can be randomly generated according to the following parameters:
  • the modal depth d;
  • the number L of clauses at depth d=0;
  • the number N of propositional variables;
  • the probability p with which a disjunct occurring in a clause at depth less than d is purely propositional;
  • the number of clauses C at depth d>0.
In the tests a problem set is characterized by N and p: d is fixed to 1, C is equal to L, and L is varied in such a way to cover the ``100\% satisfiable -- 100\% unsatisfiable'' transition. 100 3CNF(E) formulas are randomly generated for each point L in a problem set. For each run, we consider the CPU time the systems take for the main processing of the formula (excluding parsing and normalization) and we plot the median value. For practical reasons, a timeout mechanism stops the execution of the system on a formula after 1000 seconds of CPU time. For any point the execution of *SAT, *SAT+GH and TA+GH is stopped after the system exceeds the timeout on 51 of the 100 samples. DLP+GH instead, stops its execution if a super-majority of the first tests exceeds the timeout.

Random 3CNF(E) formulae with p=0% and d=1
4 variables 5 variables 6 variables 7 variables

Random 3CNF(E) formulae with p=50% and d=1
4 variables 5 variables 6 variables 7 variables



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