# Fair bisimulation

Henzinger TA, Rajamani S. 2000. Fair bisimulation. Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. TACAS: Tools and Algorithms for the Construction and Analysis of Systems, LNCS, vol. 1785, 299–314.

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Conference Paper | Published | English

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Author
Henzinger, Thomas AISTA ; Rajamani, Sriram
Series Title
LNCS
Abstract
Bisimulations enjoy numerous applications in the analysis of labeled transition systems. Many of these applications are based on two central observations: first, bisimilar systems satisfy the same branching-time properties; second, bisimilarity can be checked efficiently for finite-state systems. The local character of bisimulation, however, makes it difficult to address liveness concerns. Indeed, the definitions of fair bisimulation that have been proposed in the literature sacrifice locality, and with it, also efficient checkability. We put forward a new definition of fair bisimulation which does not suffer from this drawback. The bisimilarity of two systems can be viewed in terms of a game played between a protagonist and an adversary. In each step of the infinite bisimulation game, the adversary chooses one system, makes a move, and the protagonist matches it with a move of the other system. Consistent with this game-based view, we call two fair transition systems bisimilar if in the bisimulation game, the infinite path produced in the first system is fair iff the infinite path produced in the second system is fair. We show that this notion of fair bisimulation enjoys the following properties. First, fairly bisimilar systems satisfy the same formulas of the logics Fair-AFMC (the fair alternation-free μ-calculus) and Fair-CTL*. Therefore, fair bisimulations can serve as property-preserving abstractions for these logics and weaker ones, such as Fair-CTL and LTL. Indeed, Fair-AFMC provides an exact logical characterization of fair bisimilarity. Second, it can be checked in time polynomial in the number of states if two systems are fairly bisimilar. This is in stark contrast to all trace-based equivalences, which are traditionally used for addressing liveness but require exponential time for checking.
Publishing Year
Date Published
2000-01-01
Proceedings Title
Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Acknowledgement
This research was supported in part by the DARPA (NASA) grant NAG2-1214, the SRC contract 99-TJ-683.003, the MARCO grant 98-DT-660, the DARPA (MARCO) grant MDA972-99-1-0001, and the NSF CAREER award CCR-9501708.
Volume
1785
Page
299 - 314
Conference
TACAS: Tools and Algorithms for the Construction and Analysis of Systems
Conference Location
Berlin, Germany
Conference Date
2000-03-25 – 2000-04-02
ISBN
IST-REx-ID

### Cite this

Henzinger TA, Rajamani S. Fair bisimulation. In: Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. Vol 1785. Springer; 2000:299-314. doi:10.1007/3-540-46419-0_21
Henzinger, T. A., & Rajamani, S. (2000). Fair bisimulation. In Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (Vol. 1785, pp. 299–314). Berlin, Germany: Springer. https://doi.org/10.1007/3-540-46419-0_21
Henzinger, Thomas A, and Sriram Rajamani. “Fair Bisimulation.” In Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, 1785:299–314. Springer, 2000. https://doi.org/10.1007/3-540-46419-0_21.
T. A. Henzinger and S. Rajamani, “Fair bisimulation,” in Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Berlin, Germany, 2000, vol. 1785, pp. 299–314.
Henzinger TA, Rajamani S. 2000. Fair bisimulation. Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. TACAS: Tools and Algorithms for the Construction and Analysis of Systems, LNCS, vol. 1785, 299–314.
Henzinger, Thomas A., and Sriram Rajamani. “Fair Bisimulation.” Proceedings of the 6th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, vol. 1785, Springer, 2000, pp. 299–314, doi:10.1007/3-540-46419-0_21.

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