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 0/8/0 2.73 2708 3007
C20-V4-D4 0/8/0 6.89 4805 3399
C30-V4-D4 0/8/0 9.08 6383 3429
C10-V4-D6 0/8/0 2.18 1474 4129
C40-V4-D4 0/8/0 16.87 11012 3501
C20-V4-D6 0/8/0 7.66 4534 5441
C30-V4-D6 0/8/0 14.82 7395 5628
C50-V4-D4 0/8/0 20.87 14330 4027
C10-V8-D4 0/8/0 25.18 11868 6264
C40-V4-D6 0/8/0 21.95 10432 6506
C20-V8-D4 0/8/0 502.22 151215 9587
C10-V8-D6 0/8/0 53.73 20948 9938
C50-V4-D6 0/8/0 33.71 15513 6667
C30-V8-D4 0/6/2 570.79 159546 10852
C20-V8-D6 0/8/0 172.09 38982 16164
C40-V8-D4 0/3/5 655.53 164708 11309
C30-V8-D6 0/7/1 447.32 86268 20550
C50-V8-D4 0/2/6 934.99 199231 12379
C40-V8-D6 0/2/6 885.67 115207 22524
C50-V8-D6 0/2/6 1113.81 208242 24986
C10-V16-D4 0/0/8 -- 497959 --
C20-V16-D4 0/0/8 -- 150031 --
C10-V16-D6 0/3/5 375.51 95405 24267



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