# standard enumeration

The *standard enumeration* of ${\{0,1\}}^{*}$ is the sequence of strings ${s}_{0}=\lambda $, ${s}_{1}=0$, ${s}_{2}=1$, ${s}_{3}=00$, ${s}_{4}=01$, $\mathrm{\cdots}$ in lexicographic order^{}.

The *characteristic function ^{}* of a language

^{}$A$ is ${\chi}_{A}:\mathbb{N}\to \{0,1\}$ such that

$${\chi}_{A}(n)=\{\begin{array}{cc}1,\text{if}{s}_{n}\in A\hfill & \\ 0,\text{if}{s}_{n}\notin A.\hfill & \end{array}$$ |

The *characteristic sequence* of a language $A$ (also denoted as ${\chi}_{A}$) is the concatenation^{} of the values of the characteristic function in the natural order.

Title | standard enumeration |
---|---|

Canonical name | StandardEnumeration |

Date of creation | 2013-03-22 13:33:12 |

Last modified on | 2013-03-22 13:33:12 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 21 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 68Q45 |

Classification | msc 03B65 |

Synonym | lexicographic enumeration |

Defines | characteristic function |

Defines | characteristic sequence |