A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata

Rafael C. Carrasco; Jan Daciuk

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 4, page 779-790
  • ISSN: 0988-3754

Abstract

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We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA are a suitable structure to implement stable hashing schemes, that is, schemes where the output for every key can be determined prior to the automaton construction. We provide incremental procedures to build the pseudo-minimal DTA and the mapping that associates an integer value to every transition that will be used to compute the hash codes. This incremental construction allows for the incorporation of new trees and their hash codes without the need to rebuild the whole DTA from scratch.

How to cite

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Carrasco, Rafael C., and Daciuk, Jan. "A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata." RAIRO - Theoretical Informatics and Applications 43.4 (2009): 779-790. <http://eudml.org/doc/250583>.

@article{Carrasco2009,
abstract = { We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA are a suitable structure to implement stable hashing schemes, that is, schemes where the output for every key can be determined prior to the automaton construction. We provide incremental procedures to build the pseudo-minimal DTA and the mapping that associates an integer value to every transition that will be used to compute the hash codes. This incremental construction allows for the incorporation of new trees and their hash codes without the need to rebuild the whole DTA from scratch. },
author = {Carrasco, Rafael C., Daciuk, Jan},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Perfect hashing; deterministic tree automata; pseudo-minimal automata; incremental automata.; perfect hashing; pseudo-minimal automata; incremental automata},
language = {eng},
month = {9},
number = {4},
pages = {779-790},
publisher = {EDP Sciences},
title = {A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata},
url = {http://eudml.org/doc/250583},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Carrasco, Rafael C.
AU - Daciuk, Jan
TI - A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2009/9//
PB - EDP Sciences
VL - 43
IS - 4
SP - 779
EP - 790
AB - We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA are a suitable structure to implement stable hashing schemes, that is, schemes where the output for every key can be determined prior to the automaton construction. We provide incremental procedures to build the pseudo-minimal DTA and the mapping that associates an integer value to every transition that will be used to compute the hash codes. This incremental construction allows for the incorporation of new trees and their hash codes without the need to rebuild the whole DTA from scratch.
LA - eng
KW - Perfect hashing; deterministic tree automata; pseudo-minimal automata; incremental automata.; perfect hashing; pseudo-minimal automata; incremental automata
UR - http://eudml.org/doc/250583
ER -

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