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Lower bounds for modular counting by circuits with modular gates

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Abstract.

We prove that constant depth circuits, with one layer of M O D m gates at the inputs, followed by a fixed number of layers of M O D p gates, where p is prime, require exponential size to compute the M O D q function, if q is a prime that divides neither p nor m.

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Authors and Affiliations

  1. Computer Science Department, University of Massachusetts, Amherst, MA 01003, USA, e-mail: barrington@cs.umass.edu, , , , , , US

    D. A. Mix Barrington

  2. Computer Science Department, Boston College, Chestnut Hill, MA 02167, USA, e-mail: straubing@bc.edu, , , , , , US

    H. Straubing

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  1. D. A. Mix Barrington
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  2. H. Straubing
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Received: January 23, 1998.

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Mix Barrington, D., Straubing, H. Lower bounds for modular counting by circuits with modular gates. Comput. complex. 8, 258–272 (1999). https://doi.org/10.1007/s000370050030

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  • DOI: https://doi.org/10.1007/s000370050030

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