Abstract
A frontier-to-root deterministic finite-state tree automaton (DTA) can be used as a compact data structure to store collections of unranked ordered trees. DTAs are usually sparser than string automata, as most transitions are undefined and therefore, special care must be taken in order to minimize them efficiently. However, it is difficult to find simple and detailed descriptions of the minimization procedure in the published literature. Here, we fully describe a simple implementation of the standard minimization algorithm that needs a time in \(\mathcal{O}(|A|^2)\), with |A| being the size of the DTA.
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References
Brainerd, W.S.: The minimalization of tree automata. Information and Control 13(5), 484–491 (1968)
Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (1997) release (October 1rst, 2002), available on http://www.grappa.univ-lille3.fr/tata
Hopcroft, J., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison–Wesley, Reading (1979)
Blum, N.: An O(n log n) implementation of the standard method for minimizing n-state finite automata. Information Processing Letters 57(2), 65–69 (1996)
Watson, B.W.: A taxonomy of finite automata minimization algorithmes. Computing Science Note 93/44, Eindhoven University of Technology, The Netherlands (1993)
Marcus, M.P., Santorini, B., Marcinkiewicz, M.: Building a large annotated corpus of english: the penn treebank. Computational Linguistics 19, 313–330 (1993)
Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Computing 16(6), 973–989 (1987)
Carrasco, R.C., Daciuk, J., Forcada, M.L.: Incremental construction of minimal tree automata (submitted, 2007)
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Carrasco, R.C., Daciuk, J., Forcada, M.L. (2007). An Implementation of Deterministic Tree Automata Minimization. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_13
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DOI: https://doi.org/10.1007/978-3-540-76336-9_13
Publisher Name: Springer, Berlin, Heidelberg
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