Δ: Set-theoretic query language capturing LOGSPACE

  • Authors:
  • Alexander Leontjev;Vladimir Sazonov

  • Affiliations:
  • Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, 152140, Russia;Department of Computer Science, University of Liverpool, Liverpool L69 7ZF, UK E-mail: V.Sazonov@csc.liv.ac.uk

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2001

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Abstract

Two versions of a set theoretic Δ-language are considered as theoretical prototypes for database query languages with “nested”, “unstructured” data where database states and queries are represented as hereditarily-finite (HF) sets and set theoretic operations, respectively. It is shown that these versions correspond exactly to (N/D)LOGSPACE computability over HF relative to a special graph representation (encoding) of HF-sets. Such languages over sets, capturing also PTIME, were introduced in previous works, however, descriptions of LOGSPACE over HF [34] were not completely satisfactory. Here we overcome the drawbacks of the previous approaches by some new partial result on definability of a linear ordering over finite extensional acyclic graphs and present a unified and simplified approach.