Tableaux 2000 - Modalized easy/medium benchmarks

February 2000


These benchmarks are described at the Tableaux 2000 competition homepage.

They consist of modal formulas obtained by translating randomly generated quantified boolean formulas. For each test:

  • C are the of 4-literal clauses in the original QBF
  • D are the alternations of quantifiers
  • V is the maximum number of variables under the scope of each quantifier
In these benchmarks, the very first translation is preprocessed by performing some resolution steps. Therefore, the resulting benchmarks are less difficult than the unpreprocessed version. Further preprocessing is then applied to convert propositional variables into special modal formulas, in such a way that propositional complexity is turned into modal complexity.

Here we evaluate *SAT+USB performance, i.e., *SAT plus bit-matrix based caching; its distinguishing features are:

  • it can store sets of formulas encoded as sets of integers
  • it can query for subsets (supersets)
  • it can be bounded in size and, if bounded, it allows to use a FIFO politic to discharge obsolete reults
We show the geometric mean of the Cpu time taken to solve some samples of each problem. A timelimit of 1200 seconds is enforced. -- in the table, means that all the samples exceded the timelimit. Also the geometric mean of the number of Consistency checks is shown. For the samples that exceeed the timelimit we take into account the number of checks performed so far.


Test *SAT+USB
S/U/T Cpu Cons Mem
C10-V4-D4 8/0/0 0.36 750 1501
C20-V4-D4 4/4/0 1.64 2231 1736
C10-V4-D6 8/0/0 0.50 973 1691
C30-V4-D4 3/5/0 2.83 2871 1830
C20-V4-D6 8/0/0 4.86 5279 2102
C40-V4-D4 1/7/0 4.43 3461 1879
C30-V4-D6 5/3/0 22.85 16895 2449
C50-V4-D4 0/8/0 4.41 3163 2451
C10-V8-D4 8/0/0 0.77 1302 2219
C40-V4-D6 1/7/0 33.29 18658 3307
C20-V8-D4 8/0/0 12.77 10773 3230
C10-V8-D6 8/0/0 0.78 1258 2666
C50-V4-D6 0/8/0 46.07 21509 3353
C30-V8-D4 8/0/0 92.74 49964 4035
C20-V8-D6 8/0/0 22.59 16482 4139
C40-V8-D4 2/5/1 517.84 203594 4384
C30-V8-D6 5/0/3 681.74 296324 5988
C50-V8-D4 0/3/5 197.68 71422 5582
C40-V8-D6 0/0/8 -- 380903 --
C50-V8-D6 0/0/8 -- 309856 --
C10-V16-D4 8/0/0 1.29 1840 3850
C20-V16-D4 8/0/0 75.98 45052 5095
C10-V16-D6 8/0/0 1.75 2064 4850
C30-V16-D4 6/0/2 703.53 244983 7068
C20-V16-D6 8/0/0 54.70 25887 6679
C40-V16-D4 0/0/8 -- 307407 --
C30-V16-D6 5/0/3 502.92 152995 9720
C50-V16-D4 0/0/8 -- 261662 --
C40-V16-D6 0/0/8 -- 253395 --
C50-V16-D6 0/0/8 -- 180169 --



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