On Safety of Unary and Nonunary IFP Operators

— The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps. Such operators correspond exactly to recursive SQL queries. Therefore, the problem under investigation is directly related to database theory. The prob...

Full description

Saved in:
Bibliographic Details
Published in:Automatic control and computer sciences Vol. 53; no. 7; pp. 683 - 688
Main Author: Dudakov, S. M.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.12.2019
Springer Nature B.V
Subjects:
Computer Science
Control Structures and Microprogramming
Fixed points (mathematics)
Investigations
Operators
Queries
Query languages
Safety
Turing machines
Universe
arity
inflationary fixed point
safety
ISSN:0146-4116, 1558-108X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract — The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps. Such operators correspond exactly to recursive SQL queries. Therefore, the problem under investigation is directly related to database theory. The problem arises from the fact that if recursion and universe relations, e.g., addition, are simultaneously used in a SQL query, then a query evaluation can fall into an infinite loop. Moreover, such a combination makes it possible to model a universal computing device, e.g., a Turing machine. Hence, the problem of finite computability for such SQL queries is undecidable. In our previous works, we established some properties of a universe those guarantee the finite computability of any IFP-operator in the universe. In this article, we investigate a connection between an arity of IFP-operators and their safety. The main result of this article is that some results for general IFP-operators do not hold for unary ones. An instance of a universe is constructed in which all unnested unary IFP-operators are safe. However, there are unsafe binary IFP-operators in this universe. Therefore, IFP-operators can become unsafe if the arity changes. In addition, there are unsafe nested unary operators. This contrasts with the general case in which this is impossible. There are also elementary equivalent universes where the same unary IFP-operators are unsafe. This behavior is also different from the behavior of general IFP-operators.
AbstractList — The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps. Such operators correspond exactly to recursive SQL queries. Therefore, the problem under investigation is directly related to database theory. The problem arises from the fact that if recursion and universe relations, e.g., addition, are simultaneously used in a SQL query, then a query evaluation can fall into an infinite loop. Moreover, such a combination makes it possible to model a universal computing device, e.g., a Turing machine. Hence, the problem of finite computability for such SQL queries is undecidable. In our previous works, we established some properties of a universe those guarantee the finite computability of any IFP-operator in the universe. In this article, we investigate a connection between an arity of IFP-operators and their safety. The main result of this article is that some results for general IFP-operators do not hold for unary ones. An instance of a universe is constructed in which all unnested unary IFP-operators are safe. However, there are unsafe binary IFP-operators in this universe. Therefore, IFP-operators can become unsafe if the arity changes. In addition, there are unsafe nested unary operators. This contrasts with the general case in which this is impossible. There are also elementary equivalent universes where the same unary IFP-operators are unsafe. This behavior is also different from the behavior of general IFP-operators.
Abstract—The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps. Such operators correspond exactly to recursive SQL queries. Therefore, the problem under investigation is directly related to database theory. The problem arises from the fact that if recursion and universe relations, e.g., addition, are simultaneously used in a SQL query, then a query evaluation can fall into an infinite loop. Moreover, such a combination makes it possible to model a universal computing device, e.g., a Turing machine. Hence, the problem of finite computability for such SQL queries is undecidable. In our previous works, we established some properties of a universe those guarantee the finite computability of any IFP-operator in the universe. In this article, we investigate a connection between an arity of IFP-operators and their safety. The main result of this article is that some results for general IFP-operators do not hold for unary ones. An instance of a universe is constructed in which all unnested unary IFP-operators are safe. However, there are unsafe binary IFP-operators in this universe. Therefore, IFP-operators can become unsafe if the arity changes. In addition, there are unsafe nested unary operators. This contrasts with the general case in which this is impossible. There are also elementary equivalent universes where the same unary IFP-operators are unsafe. This behavior is also different from the behavior of general IFP-operators.
Author Dudakov, S. M.
Author_xml – sequence: 1
  givenname: S. M.
  surname: Dudakov
  fullname: Dudakov, S. M.
  email: sergeydudakov@yandex.ru
  organization: Tver State University
BookMark eNp9kE1LAzEQhoNUsK3-AG8Lnldnks1ucpRitVCs0AreluxuIltqUpP00H9vagVB0dPM8L7PfI3IwDqrCblEuGYI7GYJWJQFYokSKgBWnJAhci5yBPEyIMODnB_0MzIKYQ2QNFEOSb6w2VIZHfeZM9mzVX6fKdtlj87uPovZ9ClbbLVX0flwTk6N2gR98RXHZDW9W00e8vnifja5nectK2XMadVoKjU2CA3t2o7xpkopk9Kg4Y0BRZkWgtGi5LwB0SnNtCql6ajismVjcnVsu_XufadDrNdu522aWFNWIVZQCJZc1dHVeheC16Zu-6hi72z0qt_UCPXhNfWv1yQSf5Bb37-la_9l6JEJyWtftf_e6W_oA20kc_c
CitedBy_id crossref_primary_10_1088_1742_6596_1902_1_012085
Cites_doi 10.1134/S1995080215040022
10.1016/0168-0072(86)90055-2
10.1006/jcss.1995.1051
ContentType Journal Article
Copyright Allerton Press, Inc. 2019
2019© Allerton Press, Inc. 2019
Copyright_xml – notice: Allerton Press, Inc. 2019
– notice: 2019© Allerton Press, Inc. 2019
DBID AAYXX
CITATION
JQ2
DOI 10.3103/S0146411619070034
DatabaseName CrossRef
ProQuest Computer Science Collection
DatabaseTitle CrossRef
ProQuest Computer Science Collection
DatabaseTitleList
ProQuest Computer Science Collection
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
EISSN 1558-108X
EndPage 688
ExternalDocumentID 10_3103_S0146411619070034
GroupedDBID -59
-5G
-BR
-EM
-Y2
-~C
-~X
.86
.VR
06D
0R~
0VY
1N0
23N
2J2
2JN
2JY
2KG
2KM
2LR
2VQ
2~H
30V
4.4
408
40D
40E
5GY
5VS
6NX
8TC
95-
95.
95~
96X
AAAVM
AABHQ
AACDK
AAHNG
AAIAL
AAJBT
AAJKR
AANZL
AARHV
AARTL
AASML
AATNV
AATVU
AAUYE
AAWCG
AAYIU
AAYQN
AAYTO
AAYZH
ABAKF
ABDZT
ABECU
ABFTD
ABFTV
ABHQN
ABJNI
ABJOX
ABKCH
ABMNI
ABMQK
ABNWP
ABQBU
ABSXP
ABTEG
ABTHY
ABTKH
ABTMW
ABULA
ABWNU
ABXPI
ACAOD
ACBXY
ACCUX
ACDTI
ACGFS
ACHSB
ACHXU
ACKNC
ACMDZ
ACMLO
ACOKC
ACOMO
ACPIV
ACSNA
ACZOJ
ADHHG
ADHIR
ADINQ
ADKNI
ADRFC
ADURQ
ADYFF
ADZKW
AEBTG
AEFQL
AEGAL
AEGNC
AEJHL
AEJRE
AEMSY
AEOHA
AEPYU
AETLH
AEVLU
AEXYK
AFBBN
AFFNX
AFGCZ
AFLOW
AFQWF
AFWTZ
AFZKB
AGAYW
AGDGC
AGJBK
AGMZJ
AGQMX
AGRTI
AGWIL
AGWZB
AGYKE
AHAVH
AHBYD
AHKAY
AHSBF
AI.
AIAKS
AIGIU
AIIXL
AILAN
AITGF
AJBLW
AJRNO
ALMA_UNASSIGNED_HOLDINGS
ALWAN
AMKLP
AMXSW
AMYLF
AMYQR
AOCGG
ARMRJ
AXYYD
B-.
BA0
BDATZ
BGNMA
CAG
COF
CS3
DDRTE
DNIVK
DPUIP
EBLON
EBS
EIOEI
EJD
ESBYG
FERAY
FFXSO
FIGPU
FINBP
FNLPD
FRRFC
FSGXE
FWDCC
GGCAI
GGRSB
GJIRD
GNWQR
GQ6
GQ7
H13
HF~
HG6
HLICF
HMJXF
HRMNR
HZ~
IJ-
IKXTQ
IWAJR
I~X
I~Z
J-C
JBSCW
JZLTJ
KOV
LLZTM
M4Y
MA-
NPVJJ
NQJWS
NU0
O9-
O93
O9J
P9O
PF0
PT4
QOS
R89
R9I
RNS
ROL
RPX
RSV
S16
S1Z
S27
S3B
SAP
SCO
SDH
SHX
SJYHP
SNE
SNPRN
SNX
SOHCF
SOJ
SPISZ
SRMVM
SSLCW
STPWE
SZN
T13
TN5
TSG
TUC
U2A
UG4
UOJIU
UTJUX
UZXMN
VC2
VFIZW
VH1
W48
WK8
XU3
YLTOR
Z7R
Z83
Z88
ZMTXR
~A9
AAPKM
AAYXX
ABDBE
ABFSG
ABJCF
ABRTQ
ACSTC
AEZWR
AFDZB
AFFHD
AFHIU
AFKRA
AFOHR
AHPBZ
AHWEU
AIXLP
ARAPS
ATHPR
BENPR
BGLVJ
CCPQU
CITATION
HCIFZ
K7-
M7S
PHGZM
PHGZT
PQGLB
PTHSS
JQ2
ID FETCH-LOGICAL-c369t-27be29e1b10b2dcd35b710b399f1f5bf0a23e88324655b08dae3ea69fd2a59c3
IEDL.DBID RSV
ISICitedReferencesCount 1
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000519474100011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0146-4116
IngestDate Wed Sep 17 23:58:55 EDT 2025
Sat Nov 29 05:52:09 EST 2025
Tue Nov 18 20:42:49 EST 2025
Fri Feb 21 02:36:34 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 7
Keywords arity
inflationary fixed point
safety
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c369t-27be29e1b10b2dcd35b710b399f1f5bf0a23e88324655b08dae3ea69fd2a59c3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2371170483
PQPubID 2043879
PageCount 6
ParticipantIDs proquest_journals_2371170483
crossref_citationtrail_10_3103_S0146411619070034
crossref_primary_10_3103_S0146411619070034
springer_journals_10_3103_S0146411619070034
PublicationCentury 2000
PublicationDate 2019-12-01
PublicationDateYYYYMMDD 2019-12-01
PublicationDate_xml – month: 12
  year: 2019
  text: 2019-12-01
  day: 01
PublicationDecade 2010
PublicationPlace Moscow
PublicationPlace_xml – name: Moscow
– name: New York
PublicationTitle Automatic control and computer sciences
PublicationTitleAbbrev Aut. Control Comp. Sci
PublicationYear 2019
Publisher Pleiades Publishing
Springer Nature B.V
Publisher_xml – name: Pleiades Publishing
– name: Springer Nature B.V
References KanellakisP.KuperG.ReveszP.Constraint query languagesJ. Comput. Syst. Sci.1995512652134794210.1006/jcss.1995.1051
Dudakov S.M., On safety of IFP-operators and recursive queries, Vestn. Tversk. Gos. Univ., Ser.: Prikl. Mat., 2013, no. 2, pp. 5–13.
MarkerD.Model Theory: An Introduction2002New YorkSpringer-Verlag1003.03034
CoddE.F.Relational completeness of data base sublanguages, in Database Systems1972
GurevichY.ShelahS.Fixed-point extensions of first-order logicAnn. Pure Appl. Logic19863226528086599210.1016/0168-0072(86)90055-2
DudakovS.M.On inflationary fix-point operators safetyLobachevskii J. Math.201536328331343119110.1134/S1995080215040022
Dudakov S. M., On safety of recursive queries, Vestn. Tversk. Gos. Univ., Ser.: Prikl. Mat., 2012, no. 4, pp. 71–80.
S.M. Dudakov (7169_CR4) 2015; 36
Y. Gurevich (7169_CR5) 1986; 32
7169_CR3
7169_CR2
E.F. Codd (7169_CR1) 1972
D. Marker (7169_CR7) 2002
P. Kanellakis (7169_CR6) 1995; 51
References_xml – reference: Dudakov S.M., On safety of IFP-operators and recursive queries, Vestn. Tversk. Gos. Univ., Ser.: Prikl. Mat., 2013, no. 2, pp. 5–13.
– reference: KanellakisP.KuperG.ReveszP.Constraint query languagesJ. Comput. Syst. Sci.1995512652134794210.1006/jcss.1995.1051
– reference: GurevichY.ShelahS.Fixed-point extensions of first-order logicAnn. Pure Appl. Logic19863226528086599210.1016/0168-0072(86)90055-2
– reference: MarkerD.Model Theory: An Introduction2002New YorkSpringer-Verlag1003.03034
– reference: CoddE.F.Relational completeness of data base sublanguages, in Database Systems1972
– reference: DudakovS.M.On inflationary fix-point operators safetyLobachevskii J. Math.201536328331343119110.1134/S1995080215040022
– reference: Dudakov S. M., On safety of recursive queries, Vestn. Tversk. Gos. Univ., Ser.: Prikl. Mat., 2012, no. 4, pp. 71–80.
– volume: 36
  start-page: 328
  year: 2015
  ident: 7169_CR4
  publication-title: Lobachevskii J. Math.
  doi: 10.1134/S1995080215040022
– volume: 32
  start-page: 265
  year: 1986
  ident: 7169_CR5
  publication-title: Ann. Pure Appl. Logic
  doi: 10.1016/0168-0072(86)90055-2
– ident: 7169_CR2
– volume-title: Model Theory: An Introduction
  year: 2002
  ident: 7169_CR7
– ident: 7169_CR3
– volume-title: Relational completeness of data base sublanguages, in Database Systems
  year: 1972
  ident: 7169_CR1
– volume: 51
  start-page: 26
  year: 1995
  ident: 7169_CR6
  publication-title: J. Comput. Syst. Sci.
  doi: 10.1006/jcss.1995.1051
SSID ssj0055886
Score 2.1151848
Snippet — The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps. Such...
Abstract—The article investigates the safety of unary inflationary fixed point operators (IFP-operators), i.e., their computability in finitely many steps....
SourceID proquest
crossref
springer
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 683
SubjectTerms Computer Science
Control Structures and Microprogramming
Fixed points (mathematics)
Investigations
Operators
Queries
Query languages
Safety
Turing machines
Universe
Title On Safety of Unary and Nonunary IFP Operators
URI https://link.springer.com/article/10.3103/S0146411619070034
https://www.proquest.com/docview/2371170483
Volume 53
WOSCitedRecordID wos000519474100011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAVX
  databaseName: Springer Collection (Lakeside Campuses)
  customDbUrl:
  eissn: 1558-108X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0055886
  issn: 0146-4116
  databaseCode: RSV
  dateStart: 20070201
  isFulltext: true
  titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22
  providerName: Springer Nature
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFH_o9KAHp1NxOiUHT0oxTfqRHEUcetmGm7JbSdoEBOnG1gn-9yZp6_wGPZa-hpKXl_d7vI8fwKmJKDQjEntS2JacGDNP6jjzsIi4zwVRXGBHNhH3emw85oOqj3teV7vXKUl3U7u4EtMLW4YUBb5BKCaes2NVVmHNeDtm-Rruhg_19RuGzNE7WmnPipepzO-X-OiMlgjzU1LU-Zpu819_uQ1bFbREl-VZ2IEVlbegWdM2oMqKW7D5bgbhLnj9HA2FVsULmmh0b7tzkcgz1JvkC_dw2x2g_lS5dPx8D0bd69HVjVdxKHgpjXjhkVgqwpUvfSxJlmY0lAZTSANLtK9DqbEgVDFj1naOmsQsE4oqoyedERHylO5DI5_k6gCQz9LIF8bbR1IGNl0YcqxpioWv0kjToA243sskreaLW5qLp8TEGXZvki9704azt0-m5XCN34Q7tYKSys7mCaGxpc4JGG3Dea2Q5esfFzv8k_QRbBicxMsqlg40itlCHcN6-lw8zmcn7vi9Ar1bzbM
linkProvider Springer Nature
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED90CuqD06k4nZoHn5Ri2vQrjyKODWc33JS9laRNQJBurJ3gf2_SD-c36GPpNZRcLnfH3f1-AKcqo5C-xbHBmR7J8bBvcOnFBmYuNSmzBGU4J5vwgsAfj-mgnONOq273qiSZ39R5XonJhW5Dcm1TRSgqn9OwKsuwYiuHpQHz74YP1fXrOH5O76ilDS1elDK_X-KjM1pEmJ-Kormvadf_9ZdbsFmGluiyOAvbsCSSBtQr2gZUWnEDNt5hEO6A0U_QkEmRvaCJRPd6OhexJEbBJJnnD932APWnIi_Hp7swal-PrjpGyaFgRMSlmWF5XFhUmNzE3IqjmDhcxRRchSXSlA6XmFlE-MqsNY4ax37MBBFKTzK2mEMjsge1ZJKIfUCmH7kmU97e5dzW5UKHYkkizEwRuZLYTcDVXoZRiS-uaS6eQpVn6L0Jv-xNE87ePpkW4Bq_CbcqBYWlnaWhRTxNnWP7pAnnlUIWr39c7OBP0iew1hnd9sJeN7g5hHUVM9Gio6UFtWw2F0ewGj1nj-nsOD-Kr2sQ0Jc
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD7oFNEHp1NxOjUPPilladNbHkUtDqUbbMreStImIEg31k7w35v04ryD-Fh6Eso5Oc13OJcP4FRFFNK3ODY40y05HvYNLr3EwMylJmWWoAwXZBNeGPrjMR1UPKdZXe1epyTLngY9pSnNu9NEdosYE5OuLklybVOhFRXb6REry7Bi6zp6Ha4PH-pfseP4BdWjlja0eJnW_H6LjxfTAm1-SpAW907Q_PcXb8FmBTnRRXlGtmFJpC1o1nQOqPLuFmy8m024A0Y_RUMmRf6CJhLd665dxNIEhZN0Xjz0ggHqT0WRps92YRRcjy5vjIpbwYiJS3PD8riwqDC5ibmVxAlxuMIaXMEVaUqHS8wsInzl7nq-Gsd-wgQRyn4ysZhDY7IHjXSSin1Aph-7JlMowOXc1mlEh2JJYsxMEbuS2G3AtV6juJo7rukvniIVf2jdRF9004aztyXTcujGb8Kd2lhR5X9ZZBFPU-rYPmnDeW2cxesfNzv4k_QJrA2uguiuF94ewrqCUrQsdOlAI5_NxRGsxs_5YzY7Lk7lK9Wx2Xs
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+Safety+of+Unary+and+Nonunary+IFP+Operators&rft.jtitle=Automatic+control+and+computer+sciences&rft.au=Dudakov%2C+S.+M.&rft.date=2019-12-01&rft.pub=Pleiades+Publishing&rft.issn=0146-4116&rft.eissn=1558-108X&rft.volume=53&rft.issue=7&rft.spage=683&rft.epage=688&rft_id=info:doi/10.3103%2FS0146411619070034&rft.externalDocID=10_3103_S0146411619070034
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0146-4116&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0146-4116&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0146-4116&client=summon