Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The expressive power of voting polynomials
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Polynomial threshold functions, AC0 functions, and spectral norms
SIAM Journal on Computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Explicit Constructions of Depth-2 Majority Circuits for Comparison and Addition
SIAM Journal on Discrete Mathematics
Perceptrons, PP, and the polynomial hierarchy
Computational Complexity - Special issue on circuit complexity
On the computational power of depth-2 circuits with threshold and modulo gates
Theoretical Computer Science
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
A lower bound for perceptrons and an Oracle separation of the PPPH hierarchy
Journal of Computer and System Sciences
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
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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 驴 1 the complexity class defined by polynomial length AC0k-decision lists lies strictly between AC0k+1 and AC0k+2.