Geodesic
A~generic relation on recursively enumerable sets
Algebra i logika, Tome 55 (2016) no. 5, pp. 587-596.

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

We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical $m$-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets.
Keywords: generic relation, complete set, recursively enumerable set. 
@article{AL_2016_55_5_a4,
     author = {A. N. Rybalov},
     title = {A~generic relation on recursively enumerable sets},
     journal = {Algebra i logika},
     pages = {587--596},
     publisher = {mathdoc},
     volume = {55},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/}
}
TY  - JOUR
AU  - A. N. Rybalov
TI  - A~generic relation on recursively enumerable sets
JO  - Algebra i logika
PY  - 2016
SP  - 587
EP  - 596
VL  - 55
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/
LA  - ru
ID  - AL_2016_55_5_a4
ER  - 
%0 Journal Article
%A A. N. Rybalov
%T A~generic relation on recursively enumerable sets
%J Algebra i logika
%D 2016
%P 587-596
%V 55
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/
%G ru
%F AL_2016_55_5_a4
A. N. Rybalov. A~generic relation on recursively enumerable sets. Algebra i logika, Tome 55 (2016) no. 5, pp. 587-596. http://geodesic.mathdoc.fr/item/AL_2016_55_5_a4/

[1] I. Kapovich, A. Myasnikov, P. Schupp, V. Shpilrain, “Generic-case complexity, decision problems in group theory, and random walks”, J. Algebra, 264:2 (2003), 665–694 | DOI | MR | Zbl

[2] I. Kapovich, A. Myasnikov, P. Schupp, V. Shpilrain, “Average-case complexity and decision problems in group theory”, Adv. Math., 190:2 (2005), 343–359 | DOI | MR | Zbl

[3] J. D. Hamkins, A. Miasnikov, “The halting problem is decidable on a set of asymptotic probability one”, Notre Dame J. Formal Logic, 47:4 (2006), 515–524 | DOI | MR | Zbl

[4] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR

[5] S. A. Cook, “The complexity of theorem-proving procedures”, Proc. 3rd ann. ACM Sympos. Theory Computing (Shaker Heights, Ohio, 1971), ACM, 1971, 151–158 | DOI | Zbl

[6] C. G. Jockusch (jun.), P. E. Schupp, “Generic computability, Turing degrees, and asymptotic density”, J. London Math. Soc. II Ser., 85:2 (2012), 472–490 | DOI | MR | Zbl

[7] G. Igusa, “The generic degrees of density-1 sets, and a characterization of the hyperarithmetic reals”, J. Symb. Log., 80:4 (2015), 1290–1314 | DOI | MR | Zbl