The complexity of random ordered structures

We show that for random bit strings, Up(n), with probability, p = 1 2 , the firstorder quantifier depth D(Up(n)) needed to distinguish non-isomorphic structures is (lg lg n), with high probability. Further, we show that, with high probability, for random ordered graphs, G,p(n) with edge probabiltiy p = 1 2 , D(G,p(n)) = (log n), contrasting with the results of random (non-ordered) graphs, Gp(n), by Kim et al. [5] of D(Gp(n)) = log1/p n + O(lg lg n). Key words: random graphs, random bit strings, first order logic, Ehrenfeucht-Fraisse games

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Joel H. Spencer, Katherine St. John
• Keywords: APAL 2008, Firstorder Quantifier Depth, Non-isomorphic Structures, Random Bit Strings