The complexity of random ordered structures

Annals of Pure and Applied Logic 152 (1-3):174-179 (2008)
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Abstract

We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish non-isomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? Random Structures and Algorithms 26 119–145] of D)=log1/pn+O.

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