Hilbert's Thirteenth Problem and Circuit Complexity
نویسندگان
چکیده
We study the following question, communicated to us by Miklós Ajtai: Can all explicit (e.g., polynomial time computable) functions f : ({0, 1}) → {0, 1} 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}) and each gate G computes some binary operation gG : ({0, 1}) → {0, 1}, 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 ACC circuits.
منابع مشابه
Hilbert’s Thirteenth Problem
Some progress is made in Hilbert’s Thirteenth problem. Résumé Un certain progrès est réalisé dans le treizième problème de Hilbert.
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