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Abstract: The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space. This proves that in general the powerset is an intractable operator for implementing fixpoint queries. 1 Introduction Abiteboul and Beeri in [AB88] have shown that powerset can express transitive closure... (Update)
Context of citations to this paper: More
...those that contain a given one and are transitive. Of course this way of computing tc uses exponential space. A remarkable result of [SP94] says that no matter how we write an A B expression to compute tc, it will use exponential space. However, it is based on a contrived...
...in the complex value algebra, calculus, and method schema frameworks. In the complex value algebra, we reconsider a nice result of [SP94] that states that any algebraic query expressing transitive closure essentially requires exponential space if evaluated naturally. We...
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BibTeX entry: (Update)
D. Suciu and J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, Proc. ACM Symp. on Principles of Database Systems, 1994, pp. 171--179. http://citeseer.ist.psu.edu/suciu94any.html More
@inproceedings{ suciu94any,
author = "Dan Suciu and Jan Paredaens",
title = "Any Algorithm in the Complex Object Algebra with Powerset Needs Exponential Space to Compute Transitive Closure",
pages = "201--209",
year = "1994",
url = "citeseer.ist.psu.edu/suciu94any.html" }
Citations (may not include all citations):1911 Introduction to automata theory (context) - Hopcroft, Ullman - 1979
233 Natural semantics (context) - Kahn - 1987
211 Languages that capture complexity classes - Immerman - 1987
163 Universality of data retrieval languages (context) - Aho, Ullman - 1979
134 The relational model with relation-valued attributes (context) - Schek, Scholl - 1986
129 the power of languages for the manipulation of complex objec.. - Abiteboul, Beeri - 1988
114 Generic computation and its complexity (context) - Abiteboul, Vianu - 1991
106 Naturally embedded query languages (context) - Breazu-Tannen, Buneman et al. - 1992
78 Nested relational structures (context) - Thomas, Fischer - 1986
60 On uniformity within NC (context) - Barrington, Immerman et al. - 1990
60 Normal forms and conservative properties for query languages.. - Wong - 1993
45 Expressibility and parallel complexity - Immerman - 1989
44 the expressive power of database queries with intermediate t.. (context) - Hull, Su - 1991
39 Converting nested relational algebra expressions into flat a.. (context) - Paredaens, Van Gucht - 1992
26 Graph Theory: An Introductory Course (context) - Bollobas - 1979
18 the complexity of queries in the logical data model - Kuper, Vardi - 1993
17 A query language for NC - Suciu, Breazu-Tannen - 1994
17 Possibilities and limitations of using flat operators in nes.. (context) - Paredaens, Van Gucht - 1988
2 Mathematical Logic---A First Course (context) - Robbin - 1969
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