Standard
Bounded Reducibility for Computable Numberings. / Bazhenov, Nikolay; Mustafa, Manat; Ospichev, Sergei.
Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings. ed. / Florin Manea; Barnaby Martin; Daniël Paulusma; Giuseppe Primiero. Springer-Verlag GmbH and Co. KG, 2019. p. 96-107 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11558 LNCS).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Harvard
Bazhenov, N, Mustafa, M
& Ospichev, S 2019,
Bounded Reducibility for Computable Numberings. in F Manea, B Martin, D Paulusma & G Primiero (eds),
Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11558 LNCS, Springer-Verlag GmbH and Co. KG, pp. 96-107, 15th Conference on Computability in Europe, CiE 2019, Durham, United Kingdom,
15.07.2019.
https://doi.org/10.1007/978-3-030-22996-2_9
APA
Bazhenov, N., Mustafa, M.
, & Ospichev, S. (2019).
Bounded Reducibility for Computable Numberings. In F. Manea, B. Martin, D. Paulusma, & G. Primiero (Eds.),
Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings (pp. 96-107). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11558 LNCS). Springer-Verlag GmbH and Co. KG.
https://doi.org/10.1007/978-3-030-22996-2_9
Vancouver
Bazhenov N, Mustafa M
, Ospichev S.
Bounded Reducibility for Computable Numberings. In Manea F, Martin B, Paulusma D, Primiero G, editors, Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings. Springer-Verlag GmbH and Co. KG. 2019. p. 96-107. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-22996-2_9
Author
Bazhenov, Nikolay ; Mustafa, Manat
; Ospichev, Sergei. /
Bounded Reducibility for Computable Numberings. Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings. editor / Florin Manea ; Barnaby Martin ; Daniël Paulusma ; Giuseppe Primiero. Springer-Verlag GmbH and Co. KG, 2019. pp. 96-107 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
BibTeX
@inproceedings{8a31fae7e31a4e1693f3556b2f31be71,
title = "Bounded Reducibility for Computable Numberings",
abstract = "The theory of numberings gives a fruitful approach to studying uniform computations for various families of mathematical objects. The algorithmic complexity of numberings is usually classified via the reducibility ≤ between numberings. This reducibility gives rise to an upper semilattice of degrees, which is often called the Rogers semilattice. For a computable family S of c.e. sets, its Rogers semilattice R(S) contains the ≤ -degrees of computable numberings of S. Khutoretskii proved that R(S) is always either one-element, or infinite. Selivanov proved that an infinite R(S) cannot be a lattice. We introduce a bounded version of reducibility between numberings, denoted by ≤ bm. We show that Rogers semilattices Rbm(S), induced by ≤ bm, exhibit a striking difference from the classical case. We prove that the results of Khutoretskii and Selivanov cannot be extended to our setting: For any natural number n≥ 2, there is a finite family S of c.e. sets such that its semilattice Rbm(S) has precisely 2 n- 1 elements. Furthermore, there is a computable family T of c.e. sets such that Rbm(T) is an infinite lattice.",
author = "Nikolay Bazhenov and Manat Mustafa and Sergei Ospichev",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-22996-2_9",
language = "English",
isbn = "9783030229955",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag GmbH and Co. KG",
pages = "96--107",
editor = "Florin Manea and Barnaby Martin and Dani{\"e}l Paulusma and Giuseppe Primiero",
booktitle = "Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings",
address = "Germany",
note = "15th Conference on Computability in Europe, CiE 2019 ; Conference date: 15-07-2019 Through 19-07-2019",
}
RIS
TY - GEN
T1 - Bounded Reducibility for Computable Numberings
AU - Bazhenov, Nikolay
AU - Mustafa, Manat
AU - Ospichev, Sergei
PY - 2019/1/1
Y1 - 2019/1/1
N2 - The theory of numberings gives a fruitful approach to studying uniform computations for various families of mathematical objects. The algorithmic complexity of numberings is usually classified via the reducibility ≤ between numberings. This reducibility gives rise to an upper semilattice of degrees, which is often called the Rogers semilattice. For a computable family S of c.e. sets, its Rogers semilattice R(S) contains the ≤ -degrees of computable numberings of S. Khutoretskii proved that R(S) is always either one-element, or infinite. Selivanov proved that an infinite R(S) cannot be a lattice. We introduce a bounded version of reducibility between numberings, denoted by ≤ bm. We show that Rogers semilattices Rbm(S), induced by ≤ bm, exhibit a striking difference from the classical case. We prove that the results of Khutoretskii and Selivanov cannot be extended to our setting: For any natural number n≥ 2, there is a finite family S of c.e. sets such that its semilattice Rbm(S) has precisely 2 n- 1 elements. Furthermore, there is a computable family T of c.e. sets such that Rbm(T) is an infinite lattice.
AB - The theory of numberings gives a fruitful approach to studying uniform computations for various families of mathematical objects. The algorithmic complexity of numberings is usually classified via the reducibility ≤ between numberings. This reducibility gives rise to an upper semilattice of degrees, which is often called the Rogers semilattice. For a computable family S of c.e. sets, its Rogers semilattice R(S) contains the ≤ -degrees of computable numberings of S. Khutoretskii proved that R(S) is always either one-element, or infinite. Selivanov proved that an infinite R(S) cannot be a lattice. We introduce a bounded version of reducibility between numberings, denoted by ≤ bm. We show that Rogers semilattices Rbm(S), induced by ≤ bm, exhibit a striking difference from the classical case. We prove that the results of Khutoretskii and Selivanov cannot be extended to our setting: For any natural number n≥ 2, there is a finite family S of c.e. sets such that its semilattice Rbm(S) has precisely 2 n- 1 elements. Furthermore, there is a computable family T of c.e. sets such that Rbm(T) is an infinite lattice.
UR - http://www.scopus.com/inward/record.url?scp=85069464896&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-22996-2_9
DO - 10.1007/978-3-030-22996-2_9
M3 - Conference contribution
AN - SCOPUS:85069464896
SN - 9783030229955
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 96
EP - 107
BT - Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019, Proceedings
A2 - Manea, Florin
A2 - Martin, Barnaby
A2 - Paulusma, Daniël
A2 - Primiero, Giuseppe
PB - Springer-Verlag GmbH and Co. KG
T2 - 15th Conference on Computability in Europe, CiE 2019
Y2 - 15 July 2019 through 19 July 2019
ER -
