Book ChapterDOI
Capturing LOGSPACE over Hereditarily-Finite Sets
Alexander Leontjev,Vladimir Sazonov +1 more
- pp 156-175
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TLDR
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 theory operations.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.read more
Citations
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“Everything Is Everything” Revisited: Shapeshifting Data Types with Isomorphisms and Hylomorphisms
TL;DR: This paper is an exploration of isomorphisms between elementary data types and their extension to hereditarily finite universes through hylomorphisms derived from ranking/unranking and pairing/unpairing operations.
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Declarative Combinatorics: Isomorphisms, Hylomorphisms and Hereditarily Finite Data Types in Haskell
TL;DR: This paper is an exploration in a functional programming framework of isomorphisms between elementary data types and their extension to hereditarily finite universes through hylomorphisms derived from ranking and unranking operations.
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Design theory for advanced datamodels
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Journal ArticleDOI
Δ: Set-theoretic query language capturing LOGSPACE
TL;DR: 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 theory operations, respectively and 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.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Foundations of databases
TL;DR: This book discusses Languages, Computability, and Complexity, and the Relational Model, which aims to clarify the role of Semantic Data Models in the development of Query Language Design.