Model Enumeration of Two-Variable Logic with Quadratic Delay Complexity

Code

• github.com/mengqiaolan/model_enumeration_fo2
  OfficialIn papernone★ 2

Abstract

We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables (FO^2). Specifically, given an FO^2 sentence and a positive integer n, how can one enumerate all the models of 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 (n^2) bits to represent.

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