monotone arithmetic circuits
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scholarly journals A lower bound for monotone arithmetic circuits computing 0–1 permanent

1998 ◽  
Vol 209 (1-2) ◽  
pp. 389-398 ◽  
Author(s):  
Rimli Sengupta ◽  
H. Venkateswaran
Keyword(s):  
Lower Bound ◽  
Arithmetic Circuits ◽  
Monotone Arithmetic Circuits

scholarly journals Lower Bounds on Arithmetic Circuits via Partial Derivatives (Preliminary Version)

1995 ◽  
Vol 2 (43) ◽  
Author(s):  
Noam Nisan ◽  
Avi Wigderson
Keyword(s):  
Lower Bounds ◽  
Linear Span ◽  
Arithmetic Circuits ◽  
Multivariate Polynomials ◽  
Symmetric Polynomials ◽  
Partial Derivatives ◽  
Matrix Products ◽  
Preliminary Version ◽  
A New Technique ◽  
Monotone Arithmetic Circuits

In this paper we describe a new technique for obtaining lower bounds on<br />restricted classes of non-monotone arithmetic circuits. The heart of this technique is a complexity measure for multivariate polynomials, based on the linear span of their partial derivatives. We use the technique to obtain new lower bounds for computing symmetric polynomials and iterated matrix products.

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