@inproceedings{c6c4502f3e6441d9b3d8a1aeb130ca3a,

title = "A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function",

abstract = "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.",

keywords = "Affine disperser, Boolean circuits, Lower bounds",

author = "Find, {Magnus Gausdal} and Alexander Golovnev and Hirsch, {Edward A.} and Kulikov, {Alexander S.}",

year = "2016",

month = dec,

day = "14",

doi = "10.1109/FOCS.2016.19",

language = "English",

series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "89--98",

booktitle = "Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016",

address = "United States",

note = "57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 ; Conference date: 09-10-2016 Through 11-10-2016",

}