1987 · 157 citations · 25 references
ComputingComputer SystemsCircuit TheoryCircuit ComplexityBounded-depth CircuitsCircuit Lower BoundsThreshold CircuitsThreshold FunctionsThreshold Logic
We examine a powerful model of parallel computation: polynomial size threshold circuits of bounded depth (the gates compute threshold functions with polynomial weights). Lower bounds are given to separate polynomial size threshold circuits of depth 2 from polynomial size threshold circuits of depth 3, and from probabilistic polynomial size threshold circuits of depth 2. We also consider circuits of unreliable threshold gates, circuits of imprecise threshold gates and threshold quantifiers.
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Almost optimal lower bounds for small depth circuits
Johan Håstad · 1986 · 630 citations
∑11-Formulae on finite structures
Miklós Ajtai · Annals of Pure and Applied Logic · 1983 · 586 citations