Weighted automata define a hierarchy of terminating string rewriting systems

Gebhardt, Andreas and Waldmann, Johannes: Weighted automata define a hierarchy of terminating string rewriting systems. In: Acta cybernetica, (19) 2. pp. 295-312. (2009)

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Abstract

The "matrix method" (Hofbauer and Waldmann 2006) proves termination of string rewriting via linear monotone interpretation into the domain of vectors over suitable semirings. Equivalently, such an interpretation is given by a weighted finite automaton. This is a general method that has as parameters the choice of the semiring and the dimension of the matrices (equivalently, the number of states of the automaton). We consider the semirings of nonnegative integers, rationals, algebraic numbers, and reals; with the standard operations and ordering. Monotone interpretations also allow to prove relative termination, which can be used for termination proofs that consist of several steps. The number of steps gives another hierarchy parameter. We formally define the hierarchy and we prove that it is infinite in both directions (dimension and steps).

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2009
Volume: 19
Number: 2
ISSN: 0324-721X
Page Range: pp. 295-312
Language: angol
Event Title: Weighted Automata: Theory and Applications, 2008, Dresden
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: p. 311-312.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Jun. 06. 10:15
URI: http://acta.bibl.u-szeged.hu/id/eprint/12867

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