Abstract
Tree series transformations computed by polynomial top-down and bottom-up tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izz-semirings (izz abbreviates idempotent, zero-sum and zero-divisor free) is generalized to arbitrary positive (i.e., zero-sum and zero-divisor free) commutative semirings. The latter class of semirings includes prominent examples such as the natural numbers semiring and the least common multiple semiring, which are not members of the former class.
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References
Kuich, W.: Tree transducers and formal tree series. Acta Cybernet. 14, 135–149 (1999)
Engelfriet, J., Fülöp, Z., Vogler, H.: Bottom-up and top-down tree series transformations. J. Autom. Lang. Combin. 7, 11–70 (2002)
Fülöp, Z., Vogler, H.: Tree series transformations that respect copying. Theory Comput. Systems 36, 247–293 (2003)
Kuich, W.: Formal power series over trees. In: Bozapalidis, S. (ed.) Proc. 3rd Int. Conf. Develop. in Lang. Theory, pp. 61–101. Aristotle University of Thessaloniki (1998)
Bozapalidis, S.: Equational elements in additive algebras. Theory Comput. Systems 32, 1–33 (1999)
Ésik, Z., Kuich, W.: Formal tree series. J. Autom. Lang. Combin. 8, 219–285 (2003)
Borchardt, B., Vogler, H.: Determinization of finite state weighted tree automata. J. Autom. Lang. Combin. 8, 417–463 (2003)
Droste, M., Pech, C., Vogler, H.: A Kleene theorem for weighted tree automata. Theory Comput. Systems 38, 1–38 (2005)
Berstel, J., Reutenauer, C.: Recognizable formal power series on trees. Theoret. Comput. Sci. 18, 115–148 (1982)
Borchardt, B.: The Theory of Recognizable Tree Series. PhD thesis, Technische Universität Dresden (2005)
Graehl, J., Knight, K.: Training tree transducers. In: Human Lang. Tech. Conf. of the North American Chapter of the Assoc. for Computational Linguistics, pp. 105–112 (2004)
Engelfriet, J.: The copying power of one-state tree transducers. J. Comput. System Sci. 25, 418–435 (1982)
Raoult, J.-C.: A survey of tree transductions. In: Nivat, M., Podelski, A. (eds.) Tree Automata and Languages. Elsevier Science, Amsterdam (1992)
Fülöp, Z., Gazdag, Z., Vogler, H.: Hierarchies of tree series transformations. Theoret. Comput. Sci. 314, 387–429 (2004)
Hebisch, U., Weinert, H.J.: Semirings—Algebraic Theory and Applications in Computer Science. World Scientific, Singapore (1998)
Golan, J.S.: Semirings and their Applications. Kluwer Academic, Dordrecht (1999)
Bozapalidis, S.: Context-free series on trees. Inform. and Comput. 169, 186–229 (2001)
Engelfriet, J.: Three hierarchies of transducers. Math. Systems Theory 15, 95–125 (1982)
Maletti, A.: The power of tree series transducers of type I and II. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 338–349. Springer, Heidelberg (2005)
Engelfriet, J.: Bottom-up and top-down tree transformations—a comparison. Math. Systems Theory 9, 198–231 (1975)
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Maletti, A. (2006). Hierarchies of Tree Series Transformations Revisited. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_20
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DOI: https://doi.org/10.1007/11779148_20
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