| Issue |
RAIRO-Theor. Inf. Appl.
Volume 34, Number 1, January/February 2000
|
|
|---|---|---|
| Page(s) | 39 - 46 | |
| DOI | https://doi.org/10.1051/ita:2000105 | |
| Published online | 15 April 2002 | |
Threshold Circuits for Iterated Matrix Product and Powering
1
Dipartimento di Informatica, Sist. e Com.,
Università degli Studi di Milano -Bicocca,
Via Bicocca degli Arcimboldi 8,
20126 Milano, Italy;
e-mail: mereghetti@disco.unimib.it
2
Dipartimento di Informatica,
Università degli Studi di Torino,
Corso Svizzera 185,
10149 Torino, Italy;
e-mail: beatrice@di.unito.it
Received:
20
January
1999
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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