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Compact serialization of Prolog terms (with catalan skeletons, cantor tupling and Gödel numberings)

Published online by Cambridge University Press:  25 September 2013

PAUL TARAU
PAUL TARAU*
Affiliation:
Department of Computer Science and Engineering (e-mail: tarau@cs.unt.edu)
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Abstract

We describe a compact serialization algorithm mapping Prolog terms to natural numbers of bit-sizes proportional to the memory representation of the terms. The algorithm is a ‘no bit lost’ bijection, as it associates to each Prolog term a unique natural number and each natural number corresponds to a unique syntactically well-formed term.

To avoid an exponential explosion resulting from bijections mapping term trees to natural numbers, we separate the symbol content and the syntactic skeleton of a term that we serialize compactly using a ranking algorithm for Catalan families.

A novel algorithm for the generalized Cantor bijection between ${\mathbb{N}$ and ${\mathbb{N}$k is used in the process of assigning polynomially bounded Gödel numberings to various data objects involved in the translation.

Keywords

bijective serialization of Prolog termsranking/unranking of Catalan familiesgeneralized Cantor n-tupling bijectioncombinatorial number system
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Issue 4-5: 29th International Conference on Logic Programming , July 2013 , pp. 847 - 861
Copyright
Copyright © 2013 [PAUL TARAU] 

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