Simulation for lattice-valued doubly labeled transition systems

During the last decades, a large amount of multi-valued transition systems, whose transitions or states are labeled with specific weights, have been proposed to analyze quantitative behaviors of reactive systems. To set up a unified framework to model and analyze systems with quantitative informatio...

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Bibliographic Details
Published in:International journal of approximate reasoning 2014-03, Vol.55 (3), p.797-811
Main Authors: Pan, Haiyu, Cao, Yongzhi, Zhang, Min, Chen, Yixiang
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorics. Ordered structures
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Exact sciences and technology
Fuzzy automata
Hennessy–Milner logic
Logical, boolean and switching functions
Mathematics
Order, lattices, ordered algebraic structures
Residuated lattices
Sciences and techniques of general use
Simulation
Software
Theoretical computing
Transition systems
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Summary:During the last decades, a large amount of multi-valued transition systems, whose transitions or states are labeled with specific weights, have been proposed to analyze quantitative behaviors of reactive systems. To set up a unified framework to model and analyze systems with quantitative information, in this paper, we present an extension of doubly labeled transition systems in the framework of residuated lattices, which we will refer to as lattice-valued doubly labeled transition systems (LDLTSs). Our model can be specialized to fuzzy automata over complete residuated lattices, fuzzy transition systems, and multi-valued Kripke structures. In contrast to the traditional yes/no approach to similarity, we then introduce lattice-valued similarity between LDLTSs to measure the degree of closeness of two systems, which is a value from a residuated lattice. Further, we explore the properties of robustness and compositionality of the lattice-valued similarity. Finally, we extend the Hennessy–Milner logic to the residuate lattice-valued setting and show that the obtained logic is adequate and expressive with lattice-valued similarity. •Lattice-valued doubly labeled transition systems (LDLTSs) to model systems with quantitative information.•Lattice-valued similarity between LDLTSs.•Logical characterization of lattice-valued similarity.•Robustness and compositionality of lattice-valued similarity.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2013.11.009