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

Magnus Gausdal Find; Alexander Golovnev; Edward A. Hirsch; Alexander S. Kulikov

doi:10.1109/FOCS.2016.19

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

Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

41 Scopus citations

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.

Original language	English
Title of host publication	Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
Publisher	IEEE Computer Society
Pages	89-98
Number of pages	10
ISBN (Electronic)	9781509039333
DOIs	https://doi.org/10.1109/FOCS.2016.19
State	Published - 14 Dec 2016
Externally published	Yes
Event	57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, United States Duration: 9 Oct 2016 → 11 Oct 2016

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	2016-December
ISSN (Print)	0272-5428

Conference

Conference	57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
Country/Territory	United States
City	New Brunswick
Period	9/10/16 → 11/10/16

Keywords

Affine disperser
Boolean circuits
Lower bounds

Access to Document

10.1109/FOCS.2016.19

Cite this

Find, M. G., Golovnev, A., Hirsch, E. A., & Kulikov, A. S. (2016). A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function. In Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 (pp. 89-98). Article 7782921 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2016-December). IEEE Computer Society. https://doi.org/10.1109/FOCS.2016.19

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Find, MG, Golovnev, A, Hirsch, EA & Kulikov, AS 2016, A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function. in Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016., 7782921, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2016-December, IEEE Computer Society, pp. 89-98, 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016, New Brunswick, United States, 9/10/16. https://doi.org/10.1109/FOCS.2016.19

A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function. / Find, Magnus Gausdal; Golovnev, Alexander; Hirsch, Edward A. et al.
Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016. IEEE Computer Society, 2016. p. 89-98 7782921 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2016-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

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