127 research outputs found
Computing Crisp Bisimulations for Fuzzy Structures
Fuzzy structures such as fuzzy automata, fuzzy transition systems, weighted
social networks and fuzzy interpretations in fuzzy description logics have been
widely studied. For such structures, bisimulation is a natural notion for
characterizing indiscernibility between states or individuals. There are two
kinds of bisimulations for fuzzy structures: crisp bisimulations and fuzzy
bisimulations. While the latter fits to the fuzzy paradigm, the former has also
attracted attention due to the application of crisp equivalence relations, for
example, in minimizing structures. Bisimulations can be formulated for fuzzy
labeled graphs and then adapted to other fuzzy structures. In this article, we
present an efficient algorithm for computing the partition corresponding to the
largest crisp bisimulation of a given finite fuzzy labeled graph. Its
complexity is of order , where , and are
the number of vertices, the number of nonzero edges and the number of different
fuzzy degrees of edges of the input graph, respectively. We also study a
similar problem for the setting with counting successors, which corresponds to
the case with qualified number restrictions in description logics and graded
modalities in modal logics. In particular, we provide an efficient algorithm
with the complexity for the considered problem in
that setting
Limited bisimulations for nondeterministic fuzzy transition systems
The limited version of bisimulation, called limited approximate bisimulation,
has recently been introduced to fuzzy transition systems (NFTSs). This article
extends limited approximate bisimulation to NFTSs, which are more general
structures than FTSs, to introduce a notion of -limited
-bisimulation by using an approach of relational lifting, where is
a natural number and . To give the algorithmic
characterization, a fixed point characterization of -limited
-bisimilarity is first provided. Then -limited -bisimulation
vector with -th element being a -limited -bisimulation is
introduced to investigate conditions for two states to be -limited
-bisimilar, where . Using these results, an
O(2k^2|V|^6\cdot\left|\lra\right|^2) algorithm is designed for computing the
degree of similarity between two states, where is the number of states of
the NFTS and \left|\lra\right| is the greatest number of transitions from
states. Finally, the relationship between -limited -bisimilar and
-bisimulation under is showed, and by which, a logical
characterization of -limited -bisimilarity is provided
Approximate State Reduction of Fuzzy Finite Automata
In this paper we introduce a new type of approximate state reductions where
the behaviors of the reduced and the original automaton do not have to be
identical, but they must match on all words of length less than or equal to
some given natural number. We provide four methods for performing such
reductions.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Fuzzy automata as coalgebras
The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.This work has been supported by the Guangdong Science and Technology Department
(Grant No. 2018B010107004) and the National Natural Science Foundation of China under grant No.
61772038, 61532019 and 61272160. L.S.B. was supported by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and InternationalisationCOMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT,
within project KLEE - POCI-01-0145-FEDER-030947
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