### Abstract

We show that for random bit strings, Up(n), with probability, p=12, the first-order quantifier depth D(Up(n)) needed to distinguish non-isomorphic structures is Θ(lglgn), with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p(n) with edge probabiltiy p=12, D(G≤,p(n))=Θ(log*n), contrasting with the results of random (non-ordered) graphs, Gp(n), by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? (2005), to appear in Random Structures and Algorithms] of D(Gp(n))=log1/pn+O(lglgn).

Original language | English (US) |
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Pages (from-to) | 197-206 |

Number of pages | 10 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 143 |

Issue number | SPEC. ISS. |

DOIs | |

State | Published - Jan 6 2006 |

### Keywords

- Ehrenfeucht-Fraisse games
- First order logic
- Random bit strings
- Random graphs

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Spencer, J. H., & St. John, K. (2006). The complexity of random ordered structures.

*Electronic Notes in Theoretical Computer Science*,*143*(SPEC. ISS.), 197-206. https://doi.org/10.1016/j.entcs.2005.05.030