TY - GEN

T1 - A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function

AU - Find, Magnus Gausdal

AU - Golovnev, Alexander

AU - Hirsch, Edward A.

AU - Kulikov, Alexander S.

N1 - Publisher Copyright:
© 2016 IEEE.

PY - 2016/12/14

Y1 - 2016/12/14

N2 - We consider Boolean circuits over the full binary basis. We prove a (3+1/86)n-o(n) lower bound onthe size of such a circuit for an explicitly definedpredicate, namely an affine disperser for sublinear dimension. This improves the 3n-o(n) bound of Norbert Blum (1984).The proof is based on the gate elimination technique extended with the following three ideas. We generalize the computational model by allowing circuits to contain cycles, this in turn allows us to perform affine substitutions. We use a carefully chosen circuit complexity measure to track the progress of the gate elimination process. Finally, we use quadratic substitutions that may be viewed as delayed affine substitutions.

AB - We consider Boolean circuits over the full binary basis. We prove a (3+1/86)n-o(n) lower bound onthe size of such a circuit for an explicitly definedpredicate, namely an affine disperser for sublinear dimension. This improves the 3n-o(n) bound of Norbert Blum (1984).The proof is based on the gate elimination technique extended with the following three ideas. We generalize the computational model by allowing circuits to contain cycles, this in turn allows us to perform affine substitutions. We use a carefully chosen circuit complexity measure to track the progress of the gate elimination process. Finally, we use quadratic substitutions that may be viewed as delayed affine substitutions.

KW - Affine disperser

KW - Boolean circuits

KW - Lower bounds

UR - http://www.scopus.com/inward/record.url?scp=85009344853&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2016.19

DO - 10.1109/FOCS.2016.19

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AN - SCOPUS:85009344853

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 89

EP - 98

BT - Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016

PB - IEEE Computer Society

T2 - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016

Y2 - 9 October 2016 through 11 October 2016

ER -