scholarly journals Boolean Circuit Complexity of Regular Languages

2014 ◽  
Vol 151 ◽  
pp. 342-354 ◽  
Author(s):  
Maris Valdats
Keyword(s):  
Circuit Complexity ◽  
Regular Languages ◽  
Boolean Circuit

Circuit Complexity of Regular Languages

2009 ◽  
Vol 45 (4) ◽  
pp. 865-879 ◽  
Author(s):  
Michal Koucký
Keyword(s):  
Circuit Complexity ◽  
Regular Languages

New upper bounds on the Boolean circuit complexity of symmetric functions

2010 ◽  
Vol 110 (7) ◽  
pp. 264-267 ◽  
Author(s):  
E. Demenkov ◽  
A. Kojevnikov ◽  
A. Kulikov ◽  
G. Yaroslavtsev
Keyword(s):  
Symmetric Functions ◽  
Circuit Complexity ◽  
Upper Bounds ◽  
Boolean Circuit

scholarly journals Information Flows, Graphs and their Guessing Numbers

10.37236/962 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Søren Riis
Keyword(s):  
Network Coding ◽  
Circuit Complexity ◽  
Information Flows ◽  
Boolean Circuit ◽  
Graph Theoretic ◽  
Common Information ◽  
Shift Problem ◽  
Cyclic Shifts ◽  
The Common ◽  
Multiuser Information Theory

Valiant's shift problem asks whether all $n$ cyclic shifts on $n$ bits can be realized if $n^{(1+\epsilon)}$ input output pairs ($\epsilon < 1$) are directly connected and there are additionally $m$ common bits available that can be arbitrary functions of all the inputs. If it could be shown that this is not realizable with $m = O({n\over \log \log n})$ common bits then a significant breakthrough in Boolean circuit complexity would follow. In this paper it is shown that in certain cases all cyclic shifts are realizable with $m=(n- n^{\epsilon})/2$ common bits. Previously, no solution with $m < n - o(n)$ was known, and Valiant had conjectured that $m < n/2$ was not achievable. The construction therefore establishes a novel way of realizing communication in the manner of Network Coding for the shift problem, but leaves the viability of the common information approach to proving lower bounds in Circuit Complexity open. The construction uses the graph-theoretic notion of guessing number. As a by-product the paper also establish an interesting link between Circuit Complexity and Network Coding, a new direction of research in multiuser information theory.

Bounds on an exponential sum arising in Boolean circuit complexity

2005 ◽  
Vol 341 (5) ◽  
pp. 279-282 ◽  
Author(s):  
Frederic Green ◽  
Amitabha Roy ◽  
Howard Straubing
Keyword(s):  
Circuit Complexity ◽  
Exponential Sum ◽  
Boolean Circuit
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