Abstract
We show that for every deterministic bottom-up tree transducer, a unique equivalent transducer can be constructed which is minimal. The construction is based on a sequence of normalizing transformations which, among others, guarantee that non-trivial output is produced as early as possible. For a deterministic bottom-up transducer where every state produces either none or infinitely many outputs, the minimal transducer can be constructed in polynomial time.
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References
Aho, A.V., Ullman, J.D.: Translations on a context-free grammar. Inform. and Control 19, 439–475 (1971)
Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)
Courcelle, B., Franchi-Zannettacci, P.: On the equivalence problem for attribute systems. Inform. and Control 52, 275–305 (1982)
Engelfriet, J.: Bottom-up and top-down tree transformations — a comparison. Math. Systems Theory 9, 198–231 (1975)
Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Systems Theory 10, 289–303 (1977)
Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. In: Book, R.V. (ed.) Formal language theory; perspectives and open problems. Academic Press, New York (1980)
Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inform. and Comput. 154, 34–91 (1999)
Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32, 950–1006 (2003)
Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inform. Proc. Letters 100, 206–212 (2006)
Engelfriet, J., Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. J. Comput. Syst. Sci. 75(5), 271–286 (2009)
Ésik, Z.: Decidability results concerning tree transducers I. Acta Cybernetica 5, 1–20 (1980)
Filiot, E., Raskin, J.-F., Reynier, P.-A., Servais, F., Talbot, J.-M.: Properties of visibly pushdown transducers (submitted 2010)
Fülöp, Z.: On attributed tree transducers. Acta Cybernetica 5, 261–279 (1981)
Fülöp, Z., Vágvölgyi, S.: Attributed tree transducers cannot induce all deterministic bottom-up tree transformations. Inform. and Comput. 116, 231–240 (1995)
Fülöp, Z., Vogler, H.: Syntax-Directed Semantics – Formal Models based on Tree Transducers. In: Brauer, W., Rozenberg, G., Salomaa, A. (eds.) EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (1998)
Gazdag, Z.: Decidability of the shape preserving property of bottom-up tree transducers. Int. J. Found. Comput. Sci. 17(2), 395–414 (2006)
Knuth, D.E.: Semantics of context-free languages. Math. Systems Theory 2, 127–145 (1968); Corrections in Math. Systems Theory 5, 95–96 (1971)
Laurence, G., Lemay, A., Niehren, J., Staworko, S., Tommasi, M.: Linear top-down tree-to-word transducers: Characterization and minimization. In: RTA (to appear 2010)
Lemay, A., Maneth, S., Niehren, J.: A learning algorithm for top-down XML transformations. In: PODS (to appear 2010)
Mohri, M.: Minimization algorithms for sequential transducers. Theor. Comput. Sci. 234, 177–201 (2000)
Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory 4, 257–287 (1970)
Seidl, H.: Single-valuedness of tree transducers is decidable in polynomial time. Theor. Comput. Sci. 106(1), 135–181 (1992)
Thatcher, J.W.: Generalized2 sequential machine maps. J. Comp. Syst. Sci. 4, 339–367 (1970)
Thatcher, J.W.: Tree automata: an informal survey. In: Aho, A.V. (ed.) Currents in the Theory of Computing, pp. 143–172. Prentice Hall, Englewood Cliffs (1973)
Zachar, Z.: The solvability of the equivalence problem for deterministic frontier-to-root tree transducers. Acta Cybernetica 4, 167–177 (1980)
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Friese, S., Seidl, H., Maneth, S. (2010). Minimization of Deterministic Bottom-Up Tree Transducers. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_18
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DOI: https://doi.org/10.1007/978-3-642-14455-4_18
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