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Communication complexity of matrix computation over finite fields

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Abstract

We investigate the communication complexity of singularity testing in a finite field, where the problem is to determine whether a given square matrixM is singular. We show that, forn×n matrices whose entries are elements of a finite field of sizep, the communication complexity of this problem is Θ(n 2 logp). Our results imply tight bounds for several other problems likedetermining the rank andcomputing the determinant.

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Authors and Affiliations

  1. Computer Science Department, New Mexico State University, 88003, Las Cruces, NM, USA

    J. I. Chu

  2. Computer Science Department, Pennsylvania State University, 16802, University Park, PA, USA

    G. Schnitger

Authors
  1. J. I. Chu
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  2. G. Schnitger
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Additional information

This research was supported in part by NSF Grant CCR-8805978 and AFOSR Grant 87-0-400.

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Chu, J.I., Schnitger, G. Communication complexity of matrix computation over finite fields. Math. Systems Theory 28, 215–228 (1995). https://doi.org/10.1007/BF01303056

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  • DOI: https://doi.org/10.1007/BF01303056

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