Abstract
We consider weighted finite transition systems (WTS) with weights from naturally ordered semirings. Such semirings comprise the natural numbers with ordinary addition and multiplication as well as distributive lattices and the max -plus-semiring. For these systems we explore the concepts of covering and cascade product. We show a cascade decomposition result for such WTS using special partitions of the state set of the system. This extends a classical result of automata theory to the weighted setting.
This research was partially supported by the DAAD-Serbia project “Weighted Automata over Semirings and Lattices” and the DFG-project “Gewichtete Automaten und gewichtete Logiken für diskrete Strukturen”, DR 202 / 11-1., The research of the last two authors is supported by Serbian Ministry of Science and Tech. Develop., Grant No. 174013.
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Droste, M., Meinecke, I., Šešelja, B., Tepavčević, A. (2012). Coverings and Decompositions of Semiring-Weighted Finite Transition Systems. In: Fuzzy Semirings with Applications to Automata Theory. Studies in Fuzziness and Soft Computing, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27641-5_11
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