Construction of tree automata from regular expressions

Dietrich Kuske; Ingmar Meinecke

RAIRO - Theoretical Informatics and Applications (2011)

  • Volume: 45, Issue: 3, page 347-370
  • ISSN: 0988-3754

Abstract

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Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov's partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automaton as well as for algorithmic improvements, we also transfer the methods of Champarnaud and Ziadi from words to trees.

How to cite

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Kuske, Dietrich, and Meinecke, Ingmar. "Construction of tree automata from regular expressions." RAIRO - Theoretical Informatics and Applications 45.3 (2011): 347-370. <http://eudml.org/doc/222013>.

@article{Kuske2011,
abstract = { Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov's partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automaton as well as for algorithmic improvements, we also transfer the methods of Champarnaud and Ziadi from words to trees. },
author = {Kuske, Dietrich, Meinecke, Ingmar},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Trees; automata; regular expressions; partial derivatives; tree automata; tree languages; synthesis of automata},
language = {eng},
month = {9},
number = {3},
pages = {347-370},
publisher = {EDP Sciences},
title = {Construction of tree automata from regular expressions},
url = {http://eudml.org/doc/222013},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Kuske, Dietrich
AU - Meinecke, Ingmar
TI - Construction of tree automata from regular expressions
JO - RAIRO - Theoretical Informatics and Applications
DA - 2011/9//
PB - EDP Sciences
VL - 45
IS - 3
SP - 347
EP - 370
AB - Since recognizable tree languages are closed under the rational operations, every regular tree expression denotes a recognizable tree language. We provide an alternative proof to this fact that results in smaller tree automata. To this aim, we transfer Antimirov's partial derivatives from regular word expressions to regular tree expressions. For an analysis of the size of the resulting automaton as well as for algorithmic improvements, we also transfer the methods of Champarnaud and Ziadi from words to trees.
LA - eng
KW - Trees; automata; regular expressions; partial derivatives; tree automata; tree languages; synthesis of automata
UR - http://eudml.org/doc/222013
ER -

References

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  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, Data Structures and Algorithms. Addison-Wesley, Reading, MA (1983).  Zbl0487.68005
  2. V. Antimirov, Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci.155 (1996) 291–319.  Zbl0872.68120
  3. G. Berry and R. Sethi, From regular expressions to deterministic automata. Theoret. Comput. Sci. 48 (1986) 117–126.  Zbl0626.68043
  4. J.A. Brzozowski, Derivatives of regular expressions. J. Assoc. Comput. Mach.11 (1964) 481–494.  Zbl0225.94044
  5. J.-M. Champarnaud and D. Ziadi, From c-continuations to new quadratic algorithms for automaton synthesis. Int. J. Algebra Comput.11 (2001) 707–735.  Zbl1024.68065
  6. J.-M. Champarnaud and D. Ziadi, Canonical derivatives, partial derivatives and finite automaton constructions. Theoret. Comput. Sci.289 (2002) 137–163.  Zbl1061.68109
  7. J.-M. Champarnaud, F. Nicart and D. Ziadi, Computing the follow automaton of an expression, in Proc. of CIAA 2004. Lect. Notes Comput. Sci.3317 (2004) 90–101.  Zbl1115.68424
  8. H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison and M. Tommasi, Tree automata techniques and applications. Available on: , release October, 12th (2007).  URIhttp://www.grappa.univ-lille3.fr/tata
  9. F. Gécseg and M. Steinby, Tree languages, in Handbook of Formal Languages3. Springer (1997) Chap. 1, 1–68.  
  10. V.M. Glushkov, The abstract theory of automata. Russian Mathematical Surveys16 (1961) 1–53.  Zbl0104.35404
  11. H. Hosoya and B. Pierce, Regular expression pattern matching for XML. SIGPLAN Not.36 (2001) 67–80.  Zbl1323.68076
  12. J. Hromkovic, S. Seibert and T. Wilke, Translating regular expressions into small ε -free nondeterministic finite automata. J. Comput. System Sci.62 (2001) 565–588.  Zbl1014.68093
  13. L. Ilie and S. Yu, Constructing NFAs by optimal use of positions in regular expressions, in Proc. of CPM 2002. Lect. Notes Comput. Sci.2373 (2002) 279–288.  Zbl1077.68669
  14. S.E. Kleene, Representations of events in nerve nets and finite automata, in Automata Studies. C.E. Shannon and J. McCarthy, Eds. Princeton University Press (1956) 3–42.  
  15. D. Kuske and I. Meinecke, Construction of tree automata from regular expressions, in Proc. of DLT 2008. Lect. Notes Comput. Sci.5257 (2008) 491–503.  Zbl1159.68018
  16. S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theoret. Comput. Sci.332 (2005) 141–177.  Zbl1070.68074
  17. R.F. McNaughton and H. Yamada, Regular expressions and state graphs for automata. IEEE Trans. Electron. Comput.9 (1960) 39–57.  Zbl0156.25501
  18. R. Paige and R.E. Tarjan, Three partition refinement algorithms. SIAM J. Comput.16 (1987) 973–989.  Zbl0654.68072
  19. J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003).  
  20. J. Sakarovitch, The language, the expression, and the (small) automaton, in Implementation and Application of Automata, 10th International Conference, CIAA 2005. Lect. Notes Comput. Sci.3845 (2005) 15–30.  Zbl1172.68526
  21. T. Suzuki and S. Okui, Hedge pattern partial derivative, in Proc. of CIAA 2009. Lect. Notes Comput. Sci.5642 (2009) 125–134.  Zbl1248.68317
  22. J.W. Thatcher and J.B. Wright, Generalized finite automata theory with application to a decision problem of second-order logic. Math. Syst. Theor.2 57–81 (1968).  Zbl0157.02201
  23. P. Van Emde Boas, Machine models and simulations, in Handbook of Theoretical Computer ScienceA. Elsevier & The MIT Press (1990) Chap. 1, 1–66.  Zbl0900.68265
  24. D. Ziadi, J.-P. Ponty and J.-M. Champarnaud, Passage d'une expression rationnelle à un automate fini non-déterministe. Bull. Belg. Math. Soc.4 (1997) 177–203.  

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