Abstract
Visibly pushdown transducers (VPTs) form a strict subclass of pushdown transducers (PTs) that extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. It has been shown that visibly pushdown languages form a robust subclass of context-free languages. Along the same line, we show that word transductions defined by VPTs enjoy strong properties, in contrast to PTs. In particular, functionality is decidable in PTime, k-valuedness is in NPTime and equivalence of (non-deterministic) functional VPTs is ExpTime-c. Those problems are undecidable for PTs. Output words of VPTs are not necessarily well-nested. We identify a general subclass of VPTs that produce well-nested words, which is closed by composition, and for which the type checking problem is decidable.
Work supported by the projects: (i) QUASIMODO (FP7- ICT-STREP-214755), (ii) GASICS (ESF-EUROCORES LogiCCC), (iii) Moves: “Fundamental Issues in Modelling, Verification and Evolution of Software”, http://moves.ulb.ac.be, a PAI program funded by the Federal Belgian Gouvernment, and (iv) ECSPER (ANR-JC09-472677) and SFINCS (ANR-07-SESU-012), two projects supported by the French National Research Agency.
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References
Alur, R.: Marrying words and trees. In: PODS. LNCS, vol. 5140, pp. 233–242. Springer, Heidelberg (2007)
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC, pp. 202–211 (2004)
Béal, M.-P., Carton, O., Prieur, C., Sakarovitch, J.: Squaring transducers: an efficient procedure for deciding functionality and sequentiality. TCS 292(1), 45–63 (2003)
Blattner, M., Head, T.: Single-valued a-transducers. JCSS 15(3), 310–327 (1977)
Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007), http://www.grappa.univ-lille3.fr/tata
Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SICOMP 32, 950–1006 (2003)
Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. IPL 100(5), 206–212 (2006)
Engelfriet, J., Vogler, H.: Macro tree transducers. JCSS 31(1), 71–146 (1985)
Filiot, E., Raskin, J.-F., Reynier, P.-A., Servais, F., Talbot, J.-M.: On functionality of visibly pushdown transducers. CoRR, abs/1002.1443 (2010)
Gurari, E.M., Ibarra, O.H.: A note on finite-valued and finitely ambiguous transducers. MST 16 (1983)
Harju, T., Ibarra, O.H., Karhumaki, J., Salomaa, A.: Some decision problems concerning semilinearity and commutation. JCSS 65 (2002)
Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. JACM 25(1), 116–133 (1978)
Inaba, K., Maneth, S.: The complexity of translation membership for macro tree transducers. CoRR, abs/0910.2315 (2009)
Koch, C., Scherzinger, S.: Attribute grammars for scalable query processing on XML streams. VLDB 16(3), 317–342 (2007)
Maneth, S., Neven, F.: Structured document transformations based on XSL. In: Connor, R.C.H., Mendelzon, A.O. (eds.) DBPL 1999. LNCS, vol. 1949, pp. 80–98. Springer, Heidelberg (2000)
Perst, T., Seidl, H.: Macro forest transducers. IPL 89(3), 141–149 (2004)
Plandowski, W.: Testing equivalence of morphisms on context-free languages. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 460–470. Springer, Heidelberg (1994)
Raskin, J.-F., Servais, F.: Visibly pushdown transducers. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 386–397. Springer, Heidelberg (2008)
Schützenberger, M.P.: Sur les relations rationnelles. In: Automata Theory and Formal Languages. LNCS, vol. 33, pp. 209–213. Springer, Heidelberg (1975)
Seidl, H.: Single-valuedness of tree transducers is decidable in polynomial time. TCS 106(1), 135–181 (1992)
Seidl, H.: Equivalence of finite-valued tree transducers is decidable. MST 27(4), 285–346 (1994)
Sénizergues, G.: T(A) = T(B)? In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 665–675. Springer, Heidelberg (1999)
Staworko, S., Laurence, G., Lemay, A., Niehren, J.: Equivalence of deterministic nested word to word transducers. In: Gȩbala, M. (ed.) FCT 2009. LNCS, vol. 5699, pp. 310–322. Springer, Heidelberg (2009)
Verma, K.N., Seidl, H., Schwentick, T.: On the complexity of equational horn clauses. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 337–352. Springer, Heidelberg (2005)
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Filiot, E., Raskin, JF., Reynier, PA., Servais, F., Talbot, JM. (2010). Properties of Visibly Pushdown Transducers. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_32
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DOI: https://doi.org/10.1007/978-3-642-15155-2_32
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