Geodesic
Complexity of the problem of being equivalent to Horn formulas
Algebra i logika, Tome 60 (2021) no. 6, pp. 575-586

Voir la notice de l'article provenant de la source Math-Net.Ru

We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, $\forall$-sentence, $\exists$-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity $k\geqslant 2$, then each of the problems mentioned is an $m$-complete $\Sigma^0_1$ set.
Keywords: Horn formula, $m$-reducibility, $\Sigma^0_1$ set. 
@article{AL_2021_60_6_a4,
     author = {N. T. Kogabaev},
     title = {Complexity of the problem of being equivalent to {Horn} formulas},
     journal = {Algebra i logika},
     pages = {575--586},
     publisher = {mathdoc},
     volume = {60},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_6_a4/}
}
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N. T. Kogabaev. Complexity of the problem of being equivalent to Horn formulas. Algebra i logika, Tome 60 (2021) no. 6, pp. 575-586. http://geodesic.mathdoc.fr/item/AL_2021_60_6_a4/