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/}
}
TY  - JOUR
AU  - N. T. Kogabaev
TI  - Complexity of the problem of being equivalent to Horn formulas
JO  - Algebra i logika
PY  - 2021
SP  - 575
EP  - 586
VL  - 60
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2021_60_6_a4/
LA  - ru
ID  - AL_2021_60_6_a4
ER  - 
%0 Journal Article
%A N. T. Kogabaev
%T Complexity of the problem of being equivalent to Horn formulas
%J Algebra i logika
%D 2021
%P 575-586
%V 60
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2021_60_6_a4/
%G ru
%F AL_2021_60_6_a4
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/

[1] S. N. Vasilev, “Metod sinteza uslovii vyvodimosti khornovskikh i nekotorykh drugikh formul”, Sib. matem. zh., 38:5 (1997), 1034–1046 | MR

[2] S. N. Vassilyev, “Logical approach to control theory and applications”, Nonlinear Anal., Theory Methods Appl., 30:4 (1997), 1927–1937 | DOI | MR | Zbl

[3] S. N. Vasilev, E. A. Cherkashin, “Intellektnoe upravlenie teleskopom”, Sib. zhurn. industr. matem., 1:2 (1998), 81–98 | MR

[4] S. N. Vassilyev, “The reduction method. I”, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 64:2 (2006), 242–252 | DOI | MR | Zbl

[5] S. N. Vassilyev, “The reduction method. II”, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods, 65:5 (2006), 939–955 | DOI | MR | Zbl

[6] S. N. Vasilev, G. M. Ponomarev, “Metody avtomatizatsii logicheskogo vyvoda i ikh primenenie v upravlenii dinamicheskimi i intellektualnymi sistemami”, Tr. IMM UrO RAN, 17, no. 2, 2011, 35–52

[7] S. N. Vasilev, A. A. Galyaev, “Logiko-optimizatsionnyi podkhod k resheniyu zadachi presledovaniya gruppy tselei”, DAN, 474:6 (2017), 675–681

[8] M. E. Buzikov, A. A. Galyaev, Yu. V. Guryev, K. B. Titov, E. I. Yakushenko, S. N. Vassilyev, “Intelligent control of autonomous and anthropocentric on-board systems”, Procedia Comput. Sci., 150 (2019), 10–18 | DOI

[9] A. Horn, “On sentences which are true of direct unions of algebras”, J. Symb. Log., 16:1 (1951), 14–21 | DOI | MR | Zbl

[10] F. Galvin, “Reduced products, Horn sentences, and decision problems”, Bull. Am. Math. Soc., 73 (1967), 59–64 | DOI | MR | Zbl

[11] Zh. A. Almagambetov, “O klassakh aksiom, zamknutykh otnositelno zadannykh privedennykh proizvedenii i stepenei”, Algebra i logika, 4:3 (1965), 71–77 | MR | Zbl

[12] Dzh. Bulos, R. Dzheffri, Vychislimost i logika, per. s angl., Mir, M., 1994

[13] S. S. Goncharov, “Problema chisla neavtoekvivalentnykh konstruktivizatsii”, Algebra i logika, 19:6 (1980), 621–639 | MR

[14] D. R. Hirschfeldt, B. Khoussainov, R. A. Shore, A. M. Slinko, “Degree spectra and computable dimensions in algebraic structures”, Ann. Pure Appl. Logic, 115:1–3 (2002), 71–113 | DOI | MR | Zbl

[15] W. Hodges, Model theory, Encycl. Math. Appl., 42, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl