A note on the use of determinant for proving lower bounds on the size of linear circuits

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Abstract

We consider computations of linear forms over R by circuits with linear gates where the absolute value coefficients are bounded by a constant. Also we consider a related concept of restricted rigidity of a matrix. We prove some lower bounds on the size of such circuits and the restricted rigidity of matrices in terms of the absolute value of the determinant of the matrix.

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1

Supported by grant no. A1019602 of the Academy of Sciences of the Czech Republic, and grant INT-9600919/ME 103(1997) under the cooperation of MŠMT, Czech Republic and NSF, USA. Main part of this work was done while visiting Istituto di Matematica Computazionale del CNR, Pisa, Italy.

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