Automata-based Representations for Infinite Graphs

Salvatore La Torre; Margherita Napoli

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 4, page 311-330
  • ISSN: 0988-3754

Abstract

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New compact representations of infinite graphs are investigated. Finite automata are used to represent labelled hyper-graphs which can be also multi-graphs. Our approach consists of a general framework where vertices are represented by a regular prefix-free language and edges are represented by a regular language and a function over tuples. We consider three different functions over tuples: given a tuple the first function returns its first difference, the second one returns its suffix and the last one returns its infixes. The first-difference function is substantially a direct generalization to infinite multi-hyper-graphs of the representation introduced by Ehrenfeucht et al. for finite graphs. This representation, though very interesting for finite graphs, turns out to be quite unsatisfactory for infinite graphs. The other two functions we consider while preserving some interesting features of their representation also achieves a high expressive power. As a matter of fact, our formalism either with the suffix or infix function results to be more powerful than the equational graphs introduced by Courcelle and the simple graphs defined by Caucal. The monadic second order theories of these two classes of graphs are undecidable, but still many interesting graph properties are decidable. The use of a regular prefix-free language to represent the vertices allows (fixed the language of the edges) to express a graph by a labelled tree, moreover, the use of finite automata to represent the edges allows the verification of graph properties.

How to cite

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La Torre, Salvatore, and Napoli, Margherita. "Automata-based Representations for Infinite Graphs." RAIRO - Theoretical Informatics and Applications 35.4 (2010): 311-330. <http://eudml.org/doc/221962>.

@article{LaTorre2010,
abstract = { New compact representations of infinite graphs are investigated. Finite automata are used to represent labelled hyper-graphs which can be also multi-graphs. Our approach consists of a general framework where vertices are represented by a regular prefix-free language and edges are represented by a regular language and a function over tuples. We consider three different functions over tuples: given a tuple the first function returns its first difference, the second one returns its suffix and the last one returns its infixes. The first-difference function is substantially a direct generalization to infinite multi-hyper-graphs of the representation introduced by Ehrenfeucht et al. for finite graphs. This representation, though very interesting for finite graphs, turns out to be quite unsatisfactory for infinite graphs. The other two functions we consider while preserving some interesting features of their representation also achieves a high expressive power. As a matter of fact, our formalism either with the suffix or infix function results to be more powerful than the equational graphs introduced by Courcelle and the simple graphs defined by Caucal. The monadic second order theories of these two classes of graphs are undecidable, but still many interesting graph properties are decidable. The use of a regular prefix-free language to represent the vertices allows (fixed the language of the edges) to express a graph by a labelled tree, moreover, the use of finite automata to represent the edges allows the verification of graph properties. },
author = {La Torre, Salvatore, Napoli, Margherita},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Infinite Graphs; Formal Languages.; formal languages; representation of infinite graphs; finite automata; equational graphs; graph classes},
language = {eng},
month = {3},
number = {4},
pages = {311-330},
publisher = {EDP Sciences},
title = {Automata-based Representations for Infinite Graphs},
url = {http://eudml.org/doc/221962},
volume = {35},
year = {2010},
}

TY - JOUR
AU - La Torre, Salvatore
AU - Napoli, Margherita
TI - Automata-based Representations for Infinite Graphs
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 311
EP - 330
AB - New compact representations of infinite graphs are investigated. Finite automata are used to represent labelled hyper-graphs which can be also multi-graphs. Our approach consists of a general framework where vertices are represented by a regular prefix-free language and edges are represented by a regular language and a function over tuples. We consider three different functions over tuples: given a tuple the first function returns its first difference, the second one returns its suffix and the last one returns its infixes. The first-difference function is substantially a direct generalization to infinite multi-hyper-graphs of the representation introduced by Ehrenfeucht et al. for finite graphs. This representation, though very interesting for finite graphs, turns out to be quite unsatisfactory for infinite graphs. The other two functions we consider while preserving some interesting features of their representation also achieves a high expressive power. As a matter of fact, our formalism either with the suffix or infix function results to be more powerful than the equational graphs introduced by Courcelle and the simple graphs defined by Caucal. The monadic second order theories of these two classes of graphs are undecidable, but still many interesting graph properties are decidable. The use of a regular prefix-free language to represent the vertices allows (fixed the language of the edges) to express a graph by a labelled tree, moreover, the use of finite automata to represent the edges allows the verification of graph properties.
LA - eng
KW - Infinite Graphs; Formal Languages.; formal languages; representation of infinite graphs; finite automata; equational graphs; graph classes
UR - http://eudml.org/doc/221962
ER -

References

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