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Capturing LOGSPACE over Hereditarily-Finite Sets

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Foundations of Information and Knowledge Systems (FoIKS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1762))

Abstract

Two versions of a set theoretic δ-language are considered as theoretical prototypes for “nested” data base query language where data base states and queries are represented, respectively, as hereditarily-finite (HF) sets and set theoretic operations. It is shown that these versions correspond exactly to (N/D)LOGSPACE computability over HF, respectively. Such languages over sets, capturing also PTIME, were introduced in previous works, however, descriptions of LOGSPACE over HF [A.Lisitsa and V.Sazonov, TCS (175) 1 (1997) pp. 183–222] were not completely satisfactory. Here we overcome the drawbacks of the previous approaches due to some new partial result on definability of a linear ordering over finite extensional acyclic graphs and present a unified and simplified approach.

The second author is supported by a grant of the Ministry of Education of Russian Federation. The final version of the paper was also prepared during his visiting in 1999 the University of Siegen, Germany.

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Authors and Affiliations

  1. Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, 152140, Russia

    Alexander Leontjev & Vladimir Sazonov

Authors
  1. Alexander Leontjev
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  2. Vladimir Sazonov
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Editors and Affiliations

  1. Institut für Informatik, Technische Universität Clausthal, Julius-Albert-Str. 4, 38678, Clausthal-Zellerfeld, Germany

    Klaus-Dieter Schewe

  2. Institut für Informatik, Technische Universität Cottbus, Postfach 101344, 03013, Cottbus, Germany

    Bernhard Thalheim

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Leontjev, A., Sazonov, V. (2000). Capturing LOGSPACE over Hereditarily-Finite Sets. In: Schewe, KD., Thalheim, B. (eds) Foundations of Information and Knowledge Systems. FoIKS 2000. Lecture Notes in Computer Science, vol 1762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46564-2_10

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  • DOI: https://doi.org/10.1007/3-540-46564-2_10

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