Random graphs and the parity quantifier

The classical zero-one law for first-order logic on random graphs says that for every first-order property in the theory of graphs and every p (0, 1), the probability that the random graph G(n, p) satisfies approaches either 0 or 1 as n approaches infinity. It is well known that this law fails to hold for any formalism that can express the parity quantifier: for certain properties, the probability that G(n, p) satisfies the property need

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Phokion G. Kolaitis, Swastik Kopparty
• Keywords: Algorithms, Classical Zero-one Law, First-order Property, Random Graphs, STOC 2009