### Abstract

Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of 3 ^{1}_{86}n-o(n). All known lower bounds are based on the so-called gate elimination technique. A typical gate elimination argument shows that it is possible to eliminate several gates from an optimal circuit by making one or several substitutions to the input variables and repeats this inductively. In this note we prove that this method cannot achieve linear bounds of cn beyond a certain constant c, where c depends only on the number of substitutions made at a single step of the induction.

Original language | English |
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Title of host publication | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |

Editors | Anca Muscholl, Piotr Faliszewski, Rolf Niedermeier |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770163 |

DOIs | |

Publication status | Published - 1 Aug 2016 |

Event | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow Duration: 22 Aug 2016 → 26 Aug 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 58 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 |
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Country | Poland |

City | Krakow |

Period | 22/08/16 → 26/08/16 |

### Fingerprint

### Scopus subject areas

- Software

### Cite this

*41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016*[46] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.46