Capturing LOGSPACE over Hereditarily-Finite Sets

  • Authors:
  • Alexander Leontjev;Vladimir Yu. Sazonov

  • Affiliations:
  • -;-

  • Venue:
  • FoIKS '00 Proceedings of the First International Symposium on Foundations of Information and Knowledge Systems
  • Year:
  • 2000

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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.