### 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 |
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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 | |

Publication status | Published - 14 Dec 2016 |

Event | 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick Duration: 9 Oct 2016 → 11 Oct 2016 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2016-December |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 |
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Country | United States |

City | New Brunswick |

Period | 9/10/16 → 11/10/16 |

### Fingerprint

### Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016*(pp. 89-98). [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