Construction of tree automata from regular expressions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 3, pp. 347-370.

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.

DOI : 10.1051/ita/2011107
Classification : 68Q45
Mots-clés : trees, automata, regular expressions, partial derivatives 
@article{ITA_2011__45_3_347_0,
     author = {Kuske, Dietrich and Meinecke, Ingmar},
     title = {Construction of tree automata from regular expressions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {347--370},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {3},
     year = {2011},
     doi = {10.1051/ita/2011107},
     mrnumber = {2836494},
     zbl = {1236.68173},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2011107/}
}
TY  - JOUR
AU  - Kuske, Dietrich
AU  - Meinecke, Ingmar
TI  - Construction of tree automata from regular expressions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2011
SP  - 347
EP  - 370
VL  - 45
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2011107/
DO  - 10.1051/ita/2011107
LA  - en
ID  - ITA_2011__45_3_347_0
ER  - 
%0 Journal Article
%A Kuske, Dietrich
%A Meinecke, Ingmar
%T Construction of tree automata from regular expressions
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2011
%P 347-370
%V 45
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2011107/
%R 10.1051/ita/2011107
%G en
%F ITA_2011__45_3_347_0
Kuske, Dietrich; Meinecke, Ingmar. Construction of tree automata from regular expressions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 3, pp. 347-370. doi : 10.1051/ita/2011107. http://www.numdam.org/articles/10.1051/ita/2011107/

[1] A.V. Aho, J.E. Hopcroft and J.D. Ullman, Data Structures and Algorithms. Addison-Wesley, Reading, MA (1983). | MR | Zbl

[2] V. Antimirov, Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155 (1996) 291-319. | MR | Zbl

[3] G. Berry and R. Sethi, From regular expressions to deterministic automata. Theoret. Comput. Sci. 48 (1986) 117-126. | MR | Zbl

[4] J.A. Brzozowski, Derivatives of regular expressions. J. Assoc. Comput. Mach. 11 (1964) 481-494. | MR | Zbl

[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. | MR | Zbl

[6] J.-M. Champarnaud and D. Ziadi, Canonical derivatives, partial derivatives and finite automaton constructions. Theoret. Comput. Sci. 289 (2002) 137-163. | MR | Zbl

[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. | MR | Zbl

[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: http://www.grappa.univ-lille3.fr/tata, release October, 12th (2007).

[9] F. Gécseg and M. Steinby, Tree languages, in Handbook of Formal Languages 3. Springer (1997) Chap. 1, 1-68. | MR

[10] V.M. Glushkov, The abstract theory of automata. Russian Mathematical Surveys 16 (1961) 1-53. | Zbl

[11] H. Hosoya and B. Pierce, Regular expression pattern matching for XML. SIGPLAN Not. 36 (2001) 67-80. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR

[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. | MR | Zbl

[16] S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theoret. Comput. Sci. 332 (2005) 141-177. | MR | Zbl

[17] R.F. Mcnaughton and H. Yamada, Regular expressions and state graphs for automata. IEEE Trans. Electron. Comput. 9 (1960) 39-57. | Zbl

[18] R. Paige and R.E. Tarjan, Three partition refinement algorithms. SIAM J. Comput. 16 (1987) 973-989. | MR | Zbl

[19] J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). | Zbl

[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. | MR | Zbl

[21] T. Suzuki and S. Okui, Hedge pattern partial derivative, in Proc. of CIAA 2009. Lect. Notes Comput. Sci. 5642 (2009) 125-134. | MR | Zbl

[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). | MR | Zbl

[23] P. Van Emde Boas, Machine models and simulations, in Handbook of Theoretical Computer Science A. Elsevier & The MIT Press (1990) Chap. 1, 1-66. | MR | Zbl

[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. | Zbl

Cité par Sources :