Computing behavioural distance for fuzzy transition systems

The behavioural distance is a more robust way of formalising behavioural similarity between states than bisimulations. The smaller the distance, the more alike the states are. It is helpful for quantitative verifications of concurrent systems. The main contribution of this paper is an effective procedure for computing behavioural distance introduced by Cao et al. (IEEE Transactions on Fuzzy Systems, 21 (2013) 735–747). The time complexity of the algorithm is O(n5 m3 lg n), where n is the number of states and m is the number of transitions in the underlying transition systems. The key step in this algorithm is to compute the distance between two distributions, which is defined as the value of a mathematical programming problem (MP). In this process, some interesting properties about solutions of a fuzzy system, which is a constraint of the MP, are discussed.