### Abstract

First the notion of r-almost s-uniform tree is introduced which includes both the case of finitely generated free groups and uniform binary trees as special cases. The goal of the paper is to study pseudorandomness of binary functions defined on r-almost s-uniform trees. The measures of pseudorandomness of binary functions are introduced; the connection between these measures is analyzed; the size of these measures for truly random binary functions is studied; binary functions with strong pseudorandom properties are constructed.

Original language | English |
---|---|

Title of host publication | Frontiers of Combinatorics and Number Theory |

Publisher | Nova Science Publishers, Inc. |

Pages | 1-26 |

Number of pages | 26 |

Volume | 2 |

ISBN (Electronic) | 9781620811399 |

ISBN (Print) | 9781619429185 |

Publication status | Published - Jan 1 2012 |

### Fingerprint

### Keywords

- Binary function
- Correlation
- Legendre symbol
- Pseudorandom
- Uniform tree

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Frontiers of Combinatorics and Number Theory*(Vol. 2, pp. 1-26). Nova Science Publishers, Inc..

**Pseudorandom binary functions on almost uniform trees.** / Gyarmati, Katalin; Hubert, Pascal; Sárközy, A.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Frontiers of Combinatorics and Number Theory.*vol. 2, Nova Science Publishers, Inc., pp. 1-26.

}

TY - CHAP

T1 - Pseudorandom binary functions on almost uniform trees

AU - Gyarmati, Katalin

AU - Hubert, Pascal

AU - Sárközy, A.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - First the notion of r-almost s-uniform tree is introduced which includes both the case of finitely generated free groups and uniform binary trees as special cases. The goal of the paper is to study pseudorandomness of binary functions defined on r-almost s-uniform trees. The measures of pseudorandomness of binary functions are introduced; the connection between these measures is analyzed; the size of these measures for truly random binary functions is studied; binary functions with strong pseudorandom properties are constructed.

AB - First the notion of r-almost s-uniform tree is introduced which includes both the case of finitely generated free groups and uniform binary trees as special cases. The goal of the paper is to study pseudorandomness of binary functions defined on r-almost s-uniform trees. The measures of pseudorandomness of binary functions are introduced; the connection between these measures is analyzed; the size of these measures for truly random binary functions is studied; binary functions with strong pseudorandom properties are constructed.

KW - Binary function

KW - Correlation

KW - Legendre symbol

KW - Pseudorandom

KW - Uniform tree

UR - http://www.scopus.com/inward/record.url?scp=85016725816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016725816&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:85016725816

SN - 9781619429185

VL - 2

SP - 1

EP - 26

BT - Frontiers of Combinatorics and Number Theory

PB - Nova Science Publishers, Inc.

ER -