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Author Ioannidis, Yannis E. ♦ Wong, Eugene
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1991
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract An algebraic framework for the study of recursion has been developed. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. It is shown that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, the query answer is able to be expressed in an explicit algebraic form within an algebraic structure. The manipulative power thus afforded has several implications on the implementation of recursive query processing algorithms. Several possible decompositions of a given operator are presented that improve the performance of the algorithms, as well as several transformations that give the ability to take into account any selections or projections that are present in a givin query. In addition, it is shown that mutual linear recursion can also be studied within a closed semiring, by using relation vectors and operator matrices. Regarding nonlinear recursion, it is first shown that Horn clauses always give rise to multilinear recursion, which can always be reduced to bilinear recursion. Bilinear recursion is then shown to form a nonassociative closed semiring. Finally, several sufficient and necessary-and-sufficient conditions for bilinear recursion to be equivalent to a linear one of a specific form are given. One of the sufficient conditions is derived by embedding to bilinear recursion in an algebra.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1991-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 38
Issue Number 2
Page Count 53
Starting Page 329
Ending Page 381


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Source: ACM Digital Library