Automatic Conjecturing of P-Recursions Using Lifted Inference

Jáchym Barvínek, Timothy van Bremen, Yuyi Wang, Filip Zelezný, Ondrej Kuzelka

Abstract: Recent progress in lifted inference algorithms has made it possible to solve many non-trivial counting tasks from enumerative combinatorics in an automated fashion, by casting them as first-order model counting problems. Algorithms for this problem typically output a single number, which is the number of models of the first-order logic sentence in question on a given domain. However, in the combinatorics setting, we are more interested in obtaining a mathematical formula that holds for any given structure size. In this paper, we show that one can use lifted inference algorithms to conjecture linear recurrences with polynomial coefficients, one such class of formulas of interest.