Abstract
The article continues a study of the complexity of an analytic tableaux algorithm for SAT. The main result is that the average number of branches in analytic tableaux of formulae of lengthn isΘ((1.09988...)n). The maximum number of branches is also studied. Both the average and worst case complexity measures are used to compare analytic tableaux and truth tables.
For the average case result the precise number of consistent branches and the precise number of inconsistent branches (for formulae of lengthn) are each expressed as multiply indexed sums whose terms involve factorials and Stirling numbers of the second kind. The asymptotic behavior of these sums is determined by adapting a classical technique for determining the asymptotic behavior of singly indexed sums whose terms involve factorials.
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Rosenthal, J.W. The expected complexity of analytic tableaux analyses in propositional calculus — II. Ann Math Artif Intell 6, 201–234 (1992). https://doi.org/10.1007/BF01531029
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DOI: https://doi.org/10.1007/BF01531029