Quantitative Simulation Games

P. Cerny, T.A. Henzinger, A. Radhakrishna, in:, Z. Manna, D. Peled (Eds.), Time For Verification: Essays in Memory of Amir Pnueli, Springer, 2010, pp. 42–60.

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Book Chapter | Published | English
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LNCS
Abstract
While a boolean notion of correctness is given by a preorder on systems and properties, a quantitative notion of correctness is defined by a distance function on systems and properties, where the distance between a system and a property provides a measure of “fit” or “desirability.” In this article, we explore several ways how the simulation preorder can be generalized to a distance function. This is done by equipping the classical simulation game between a system and a property with quantitative objectives. In particular, for systems that satisfy a property, a quantitative simulation game can measure the “robustness” of the satisfaction, that is, how much the system can deviate from its nominal behavior while still satisfying the property. For systems that violate a property, a quantitative simulation game can measure the “seriousness” of the violation, that is, how much the property has to be modified so that it is satisfied by the system. These distances can be computed in polynomial time, since the computation reduces to the value problem in limit average games with constant weights. Finally, we demonstrate how the robustness distance can be used to measure how many transmission errors are tolerated by error correcting codes.
Publishing Year
Date Published
2010-07-29
Book Title
Time For Verification: Essays in Memory of Amir Pnueli
Volume
6200
Page
42 - 60
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Cite this

Cerny P, Henzinger TA, Radhakrishna A. Quantitative Simulation Games. In: Manna Z, Peled D, eds. Time For Verification: Essays in Memory of Amir Pnueli. Vol 6200. Essays in Memory of Amir Pnueli. Springer; 2010:42-60. doi:10.1007/978-3-642-13754-9_3
Cerny, P., Henzinger, T. A., & Radhakrishna, A. (2010). Quantitative Simulation Games. In Z. Manna & D. Peled (Eds.), Time For Verification: Essays in Memory of Amir Pnueli (Vol. 6200, pp. 42–60). Springer. https://doi.org/10.1007/978-3-642-13754-9_3
Cerny, Pavol, Thomas A Henzinger, and Arjun Radhakrishna. “Quantitative Simulation Games.” In Time For Verification: Essays in Memory of Amir Pnueli, edited by Zohar Manna and Doron Peled, 6200:42–60. Essays in Memory of Amir Pnueli. Springer, 2010. https://doi.org/10.1007/978-3-642-13754-9_3.
P. Cerny, T. A. Henzinger, and A. Radhakrishna, “Quantitative Simulation Games,” in Time For Verification: Essays in Memory of Amir Pnueli, vol. 6200, Z. Manna and D. Peled, Eds. Springer, 2010, pp. 42–60.
Cerny P, Henzinger TA, Radhakrishna A. 2010. Quantitative Simulation Games. Time For Verification: Essays in Memory of Amir Pnueli. Essays in Memory of Amir Pnueli, LNCS, vol. 6200. 42–60.
Cerny, Pavol, et al. “Quantitative Simulation Games.” Time For Verification: Essays in Memory of Amir Pnueli, edited by Zohar Manna and Doron Peled, vol. 6200, Springer, 2010, pp. 42–60, doi:10.1007/978-3-642-13754-9_3.

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