Model Enumeration of Two-Variable Logic with Quadratic Delay Complexity

We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables (FO2). Specifically, given an FO2 sentence Gamma and a positive integer n, how can one enumerate all the models of Gamma over a domain of size n? In this paper, we devise a novel algorithm to address this problem. The delay complexity, the time required between producing two consecutive models, of our algorithm is quadratic in the given domain size n (up to logarithmic factors) when the sentence is fixed. This complexity is almost optimal since the interpretation of binary predicates in any model requires at least Omega(n2) bits to represent.