Satisfiability Algorithms and Lower Bounds for Boolean Formulas over Finite Bases

  • Ruiwen ChenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)


We give a #SAT algorithm for boolean formulas over arbitrary finite bases. Let \(B_k\) be the basis composed of all boolean functions on at most k inputs. For \(B_k\)-formulas on n inputs of size cn, our algorithm runs in time \(2^{n(1-\delta _{c,k})}\) for \(\delta _{c,k} = c^{-O(c^2k2^k)}\). We also show the average-case hardness of computing affine extractors using linear-size \(B_k\)-formulas.

We also give improved algorithms and lower bounds for formulas over finite unate bases, i.e., bases of functions which are monotone increasing or decreasing in each of the input variables.


Boolean formula Satisfiability algorithm Average-case lower bound Random restriction 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK

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