MK-fuzzy Automata and MSO Logics

Manfred Droste
(University of Leipzig)
Temur Kutsia
George Rahonis
(Aristotle University of Thessaloniki)
Wolfgang Schreiner

We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizable MK-fuzzy languages accepted by MK-fuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a Büchi type theorem.

In Patricia Bouyer, Andrea Orlandini and Pierluigi San Pietro: Proceedings Eighth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2017), Roma, Italy, 20-22 September 2017, Electronic Proceedings in Theoretical Computer Science 256, pp. 106–120.
Published: 6th September 2017.

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