The complexity of random ordered structures

Joel H. Spencer, Katherine St. John

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)197-206
Number of pages10
JournalElectronic Notes in Theoretical Computer Science
Issue numberSPEC. ISS.
StatePublished - Jan 6 2006


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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