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.

[1]  Tatjana Petkovic,et al.  Congruences and homomorphisms of fuzzy automata , 2006, Fuzzy Sets Syst..

[2]  Victor R. L. Shen,et al.  Knowledge Representation Using High-Level Fuzzy Petri Nets , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Hengyang Wu,et al.  Distribution-Based Behavioral Distance for Nondeterministic Fuzzy Transition Systems , 2018, IEEE Transactions on Fuzzy Systems.

[4]  Tuan-Fang Fan,et al.  Fuzzy Bisimulation for Gödel Modal Logic , 2015, IEEE Transactions on Fuzzy Systems.

[5]  Yixiang Chen,et al.  Algorithmic and logical characterizations of bisimulations for non-deterministic fuzzy transition systems , 2018, Fuzzy Sets Syst..

[6]  Yongzhi Cao,et al.  Polynomial-time Algorithms for Computing Distances of Fuzzy Transition Systems , 2017, Theor. Comput. Sci..

[7]  M. Ćiri,et al.  Computation of the greatest simulations and bisimulations between fuzzy automata , 2012 .

[8]  James Worrell,et al.  Approximating and computing behavioural distances in probabilistic transition systems , 2006, Theor. Comput. Sci..

[9]  Miroslav Ciric,et al.  Fuzzy relation equations and subsystems of fuzzy transition systems , 2013, Knowl. Based Syst..

[10]  James Worrell,et al.  The Complexity of Computing a Bisimilarity Pseudometric on Probabilistic Automata , 2014, Horizons of the Mind.

[11]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[12]  Hongyan Xing,et al.  Analysis and control of fuzzy discrete event systems using bisimulation equivalence , 2012, Theor. Comput. Sci..

[13]  James Worrell,et al.  A behavioural pseudometric for probabilistic transition systems , 2005, Theor. Comput. Sci..

[14]  Yuxin Deng,et al.  Logical characterizations of simulation and bisimulation for fuzzy transition systems , 2016, Fuzzy Sets Syst..

[15]  Weilin Deng,et al.  Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence , 2015, IEEE Transactions on Fuzzy Systems.

[16]  Orna Kupferman,et al.  Latticed Simulation Relations and Games , 2010, Int. J. Found. Comput. Sci..

[17]  King-Sun Fu,et al.  A Formulation of Fuzzy Automata and Its Application as a Model of Learning Systems , 1969, IEEE Trans. Syst. Sci. Cybern..

[18]  Miroslav Ciric,et al.  Computation of the greatest simulations and bisimulations between fuzzy automata , 2011, Fuzzy Sets Syst..

[19]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[20]  Etienne E. Kerre,et al.  Bisimulations for Fuzzy-Transition Systems , 2010, IEEE Transactions on Fuzzy Systems.

[21]  Miroslav Ciric,et al.  Bisimulations for fuzzy automata , 2011, Fuzzy Sets Syst..

[22]  Huaiqing Wang,et al.  A Behavioral Distance for Fuzzy-Transition Systems , 2011, IEEE Transactions on Fuzzy Systems.

[23]  Christel Baier,et al.  Principles of model checking , 2008 .

[24]  Feng Lin,et al.  Modeling and control of fuzzy discrete event systems , 2002, IEEE Trans. Syst. Man Cybern. Part B.