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computational complexity

, Volume 14, Issue 4, pp 362–375 | Cite as

On the computational power of Boolean decision lists

  • Matthias Krause
Original Paper

Abstract.

We study the computational power of decision lists over AND-functions versus \( \hbox{threshold-}\oplus \) circuits. AND-decision lists are a natural generalization of formulas in disjunctive or conjunctive normal form. We show that, in contrast to CNF- and DNF-formulas, there are functions with small AND-decision lists which need exponential size unbounded weight \(\hbox{threshold-}\oplus \) circuits. Consequently, it is questionable if the polynomial learning algorithm for DNFs of Jackson (1994), which is based on the efficient simulation of DNFs by polynomial weight \( \hbox{threshold-}\oplus \) circuits (Krause & Pudlák 1994), can be successfully applied to functions with small AND-decision lists. A further result is that for all k ≥ 1 the complexity class defined by polynomial length AC 0 k -decision lists lies strictly between AC 0 k+1 and AC 0 k+2.

Keywords.

Decision lists AC0 learnability lower bounds 

Subject classification.

68Q15 94C05 94C10 06E30 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Lehrstuhl Theoretische InformatikUniversität MannheimMannheimGermany

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