A pumping lemma and decidability problems for recognizable tree series

Borchardt, Björn: A pumping lemma and decidability problems for recognizable tree series. In: Acta cybernetica, (16) 4. pp. 509-544. (2004)

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Abstract

In the present paper we show that given a tree series S, which is accepted by (a) a deterministic bottom-up finite state weighted tree automaton (for short: bu-w-fta) or (b) a non-deterministic bu-w-fta over a locally finite semiring, there exists for every input tree t E supp(S) a decomposition t = C'[C[s]] into contexts C, C' and an input tree s as well as there exist semiring elements a, a', b, b', c such that the equation (S,C'[Cn[s]]) = a'OanOcObnOb' holds for every non-negative integer n. In order to prove this pumping lemma we extend the power-set construction of classical theories and show that for every non-deterministic bu-w-fta over a locally finite semiring there exists an equivalent deterministic one. By applying the pumping lemma we prove the decidability of a tree series S being constant on its support, S being constant, S being boolean, the support of S being the empty set, and the support of S being a finite set provided that S is accepted by (a) a deterministic bu-w-fta over a commutative semiring or (b) a non-deterministic bu-w-fta over a locally finite commutative semiring.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2004
Volume: 16
Number: 4
ISSN: 0324-721X
Page Range: pp. 509-544
Language: angol
Related URLs: http://acta.bibl.u-szeged.hu/38518/
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: p. 542-544.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2021. Mar. 24. 14:43
URI: http://acta.bibl.u-szeged.hu/id/eprint/12739

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