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Δ: Set-theoretic query language capturing LOGSPACE

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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.

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Authors and Affiliations

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

    Alexander Leontjev

  2. Department of Computer Science, University of Liverpool, Liverpool L69 7ZF, UK

    Vladimir Sazonov

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  1. Alexander Leontjev
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  2. Vladimir Sazonov
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Leontjev, A., Sazonov, V. Δ: Set-theoretic query language capturing LOGSPACE. Annals of Mathematics and Artificial Intelligence 33, 309–345 (2001). https://doi.org/10.1023/A:1013189515673

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