Abstract
Nondeterministic fuzzy transition systems (NFTSs) offer a robust framework for modeling and analyzing systems with inherent uncertainties and imprecision, which are prevalent in real-world scenarios. Wu et al. (2018) provided an algorithm for computing the crisp bisimilarity (the greatest crisp bisimulation) of a finite NFTS S=〈S,A,δ〉, with a time complexity of order O(|S|4⋅|δ|2) under the assumption that |δ|≥|S|. Qiao et al. (2023) provided an algorithm for computing the fuzzy bisimilarity (the greatest fuzzy bisimulation) of a finite NFTS S under the Gödel semantics, with a time complexity of order O(|S|4⋅|δ|2⋅l) under the assumption that |δ|≥|S|, where l is the number of fuzzy values used in S plus 1. In this work, we provide efficient algorithms for computing the partition corresponding to the crisp bisimilarity of a finite NFTS S, as well as the compact fuzzy partition corresponding to the fuzzy bisimilarity of S under the Gödel semantics. Their time complexities are of the order O((size(δ)logl+|S|)log(|S|+|δ|)), where l is the number of fuzzy values used in S plus 2. When |δ|≥|S|, this order is within O(|S|⋅|δ|⋅log2|δ|). The reduction of time complexity from O(|S|4⋅|δ|2) and O(|S|4⋅|δ|2⋅l) to O(|S|⋅|δ|⋅log2|δ|) is a significant contribution of this work.
Published Version
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