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Abstraction and approximation in fuzzy temporal logics and models

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Formal Aspects of Computing

Abstract

Recently, by defining suitable fuzzy temporal logics, temporal properties of dynamic systems are specified during model checking process, yet a few numbers of fuzzy temporal logics along with capable corresponding models are developed and used in system design phase, moreover in case of having a suitable model, it suffers from the lack of a capable model checking approach. Having to deal with uncertainty in model checking paradigm, this paper introduces a fuzzy Kripke model (FzKripke) and then provides a verification approach using a novel logic called Fuzzy Computation Tree Logic* (FzCTL*). Not only state space explosion is handled using well-known concepts like abstraction and bisimulation, but an approximation method is also devised as a novel technique to deal with this problem. Fuzzy program graph, a generalization of program graph and FzKripke, is also introduced in this paper in consideration of higher level abstraction in model construction. Eventually modeling, and verification of a multi-valued flip-flop is studied in order to demonstrate capabilities of the proposed models.

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Authors and Affiliations

  1. Department of Computer Engineering, Islamic Azad University (Science and Research Branch), Tehran, Iran

    Gholamreza Sotudeh & Ali Movaghar

  2. Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

    Ali Movaghar

Authors
  1. Gholamreza Sotudeh
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  2. Ali Movaghar
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Correspondence to Gholamreza Sotudeh.

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Jin Song Dong

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Sotudeh, G., Movaghar, A. Abstraction and approximation in fuzzy temporal logics and models. Form Asp Comp 27, 309–334 (2015). https://doi.org/10.1007/s00165-014-0318-7

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