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Expressive Power and Data Complexity of Query Languages for Trees and Lists


Evgeny Dantsin and Andrei Voronkov

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Abstract

We extend the traditional query languages by primitives for handling lists and trees. Our main results characterize the expressive power and data complexity of the following extended languages: (1) relational algebra with lists and trees, (2) nonrecursive Datalog with lists and trees, (3) nonrecursive Prolog with lists and trees, (4) first-order logic over lists and trees.

Languages (2)-(4) turn out to have the same expressive power; their range-restricted fragments have the same expressive power as (1). Every query in these languages is a boolean combination of range-restricted queries.

We also prove that these query languages have polynomial data complexity under any "reasonable" encoding of inputs. Furthermore, under a natural encoding of inputs, languages (2)-(4) have the same expressive power as first-order logic over finite structures, therefore their data complexity is in A Co. Thus, the use of lists and trees in nonrecursive query languages gives no gain in the expressiveness. This contrasts with a huge difference between the nonelementary program complexity of extended languages (2)-(4) and the PSPACE program complexity of their relational counterparts.

Our results partly explain why lists and trees are not so widely used in nonrecursive query languages as other collection types.


References


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Referenced by

  1. Jan Van den Bussche : Constraint databases: A tutorial introduction. SIGMOD Record 29(3) : 44-51(2000)

BIBTEX


@inproceedings{DBLP:conf/pods/DantsinV00,
  author    = {Evgeny Dantsin and
                Andrei Voronkov},
   title     = {Expressive Power and Data Complexity of Query Languages for Trees
                and Lists},
   booktitle = {Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium
                on Principles of Database Systems, May 15-17, 2000, Dallas, Texas,
                USA},
   publisher = {ACM},
   year      = {2000},
   isbn      = {1-58113-214-X},
   pages     = {157-165},
   crossref  = {DBLP:conf/pods/00},
   bibsource = {DBLP, http://dblp.uni-trier.de} } },




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