RAIRO-Theor. Inf. Appl.
Volume 34, Number 1, January/February 2000
|Page(s)||39 - 46|
|Published online||15 April 2002|
Threshold Circuits for Iterated Matrix Product and Powering
Dipartimento di Informatica, Sist. e Com.,
Università degli Studi di Milano -Bicocca,
Via Bicocca degli Arcimboldi 8,
20126 Milano, Italy;
2 Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, 10149 Torino, Italy; e-mail: firstname.lastname@example.org
Accepted: 13 March 2000
The complexity of computing, via threshold circuits, the iterated product and powering of fixed-dimension matrices with integer or rational entries is studied. We call these two problems and , respectively, for short. We prove that: (i) For , does not belong to , unless .newline (ii) For stochastic matrices : belongs to while, for , does not belong to , unless . (iii) For any k, belongs to .
Mathematics Subject Classification: 68Q05 / 68Q15 / 68Q25
Key words: Threshold circuits / iterated matrix product / matrix powering.
© EDP Sciences, 2000
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