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On the power of small-depth threshold circuits

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Abstract

We investigate the power of threshold circuits of small depth. In particular, we give functions that require exponential size unweighted threshold circuits of depth 3 when we restrict the bottom fanin. We also prove that there are monotone functionsf k that can be computed in depthk and linear size ⋎, ⋏-circuits but require exponential size to compute by a depthk−1 monotone weighted threshold circuit.

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  1. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44, Stockholm, SWEDEN

    Johan Håstad & Mikael Goldmann

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  1. Johan Håstad
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  2. Mikael Goldmann
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Håstad, J., Goldmann, M. On the power of small-depth threshold circuits. Comput Complexity 1, 113–129 (1991). https://doi.org/10.1007/BF01272517

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  • DOI: https://doi.org/10.1007/BF01272517

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