Abstract
we give an equational definition for relations over trees, show that they can be described by rational expressions and give sufficient restrictions on the generated relations to ensure the rationality of their domain and range, and their stability under inverse, composition and substitution. We get in this way “rational tree transductions” extending to the case of trees the well known rational transductions over words.
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References
A. Arnold & M. Dauchet: Morphismes et bimorphismes d'arbres, TCS20, pp. 33–93 (1982).
M. Dauchet: Transductions de foêts, bimorphismes de magmoïdes, Thèse, Université de Lille 1 (1977).
M. Dauchet & S. Tison: Algebraic complexity of Tree Languages. in Tree automata and languages, M. Nivat& A. Podelski ed., Elsevier (1992).
M. Dauchet, S. Tison, T. Heuillard, P. Lescanne: Decidability or the Confluence of Ground Term Rewriting Systems, INRIA report n. 675 (1987).
N. Dershowitz & J.-P. Jouannaud: Rewriting sytems, in Handbook of Theoretical Computer Science, Jan van Leeuwen ed., Elsevier (1990).
J. Engelfriet: Bottom-up and Top-down Tree Transformations ” A Comparison, Math. System Theory vol. 9n. 3, pp. 198–231 (1975).
F. Gecseg & M. Steinby: Tree automata, Akademiai Kiado, Budapest (1984)
A. Grazon & J.-C. Raoult: Equational sets of tree-vectors, IRISA report n. 563, Rennes (1990).
A. Habel & H.J. Kreowski: Characteristics of graph languages generated by edge replacement, TCS51, pp. 81–115 (1987).
J.-C. Raoult: A survey of tree-transductions, in Tree automata and languages, M. Nivat & A. Podelski ed., Elsevier, pp. 311–326 (1992) (and report n. 1410 INRIA-RENNES (1991)).
P. P. Schreiber: Tree-transducers and syntax-connected transductions, LNCS 33, pp. 202–208 (1975).
M. Steinby: On certain algebraically defined tree transformations, in Proc. Coll. Math. Janos Bolyai on Algebra, Combinatorics and Logic in Computer Science, Györ (Hungary), pp. 745–764 (1983).
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© 1993 Springer-Verlag Berlin Heidelberg
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Raoult, JC. (1993). Recursively defined tree transductions. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_26
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DOI: https://doi.org/10.1007/978-3-662-21551-7_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56868-1
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