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ISAAC
2009
Springer

Hilbert's Thirteenth Problem and Circuit Complexity

10 years 4 days ago
Hilbert's Thirteenth Problem and Circuit Complexity
We study the following question, communicated to us by Mikl´os Ajtai: Can all explicit (e.g., polynomial time computable) functions f : ({0, 1}w )3 → {0, 1}w be computed by word circuits of constant size? Here, a word circuit is an acyclic circuit where each wire holds a word (i.e., an element of {0, 1}w ) and each gate G computes some binary operation gG : ({0, 1}w )2 → {0, 1}w , defined for all word lengths w. As our main result, we present an explicit function so that its w’th slice for any w ≥ 8 cannot be computed by word circuits with at most 4 gates. Also, we formally relate Ajtai’s question to open problems concerning ACC0 circuits.
Kristoffer Arnsfelt Hansen, Oded Lachish, Peter Br
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where ISAAC
Authors Kristoffer Arnsfelt Hansen, Oded Lachish, Peter Bro Miltersen
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