Geodesic
Complexity of the problem of being equivalent to Horn formulas.~II
Algebra i logika, Tome 61 (2022) no. 4, pp. 469-482.

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We calculate the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an $m$-complete $\Sigma^0_1$-set.
Keywords: Horn formula, $m$-reducibility, $\Sigma^0_1$-set. 
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N. T. Kogabaev. Complexity of the problem of being equivalent to Horn formulas.~II. Algebra i logika, Tome 61 (2022) no. 4, pp. 469-482. http://geodesic.mathdoc.fr/item/AL_2022_61_4_a5/

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