Model Enumeration of Two-Variable Logic with Quadratic Delay Complexity

• URL: http://arxiv.org/abs/2505.19648v1
• Date: Mon, 26 May 2025 08:04:19 GMT
• Title: Model Enumeration of Two-Variable Logic with Quadratic Delay Complexity
• Authors: Qiaolan Meng, Juhua Pu, Hongting Niu, Yuyi Wang, Yuanhong Wang, Ondřej Kuželka,
• Abstract summary: We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables ($FO2$)<n>How can one enumerate all the models of $Gamma$ over a domain of size $n$?
• Score: 6.164137092509227
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\Gamma$ 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 $\Omega(n^2)$ bits to represent.

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