## Abstract

Irit Dinur’s proof of the PCP theorem via gap amplification (J. ACM, Vol. 54 (3) and ECCC TR05-046) has an important extension to Assignment Testers (a.k.a PCPPs). This extension is based on a corresponding extension of the gap amplification theorem from PCPs to Assignment Testers (a.k.a PCPPs). Specifically, the latter extension states that the rejection probability of an Assignment Tester can be amplified by a constant factor, at the expense of increasing the output size of the Assignment Tester by a constant factor (while retaining the alphabet). We point out a gap in the proof of this extension, and show that this gap can be bridged. We stress that the gap refers to the amplification of Assignment Testers, and the underlying issue does not arise in the case of standard PCPs. Furthermore, it seems that the issue also does not arise with respect to the applications in Dinur’s paper, but it may arise in other applications.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer |

Pages | 9-16 |

Number of pages | 8 |

ISBN (Electronic) | 978-3-030-43662-9 |

ISBN (Print) | 978-3-030-43661-2 |

DOIs | |

State | Published - 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12050 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Bibliographical note

Publisher Copyright:© Springer Nature Switzerland AG 2020.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science