Quantitative temporal simulation and refinement distances for timed systems

K. Chatterjee, V. Prabhu, IEEE Transactions on Automatic Control 60 (2015) 2291–2306.

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Journal Article | Published | English
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Abstract
We introduce quantitative timed refinement and timed simulation (directed) metrics, incorporating zenoness checks, for timed systems. These metrics assign positive real numbers which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximal timing mismatch that can arise, (2) the “steady-state” maximal timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation distances to within any desired degree of accuracy. In order to compute the values of the quantitative simulation distances, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite-state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives in graph games, and then use these algorithms to compute the values of the timed simulation distances over timed automata.
Publishing Year
Date Published
2015-02-24
Journal Title
IEEE Transactions on Automatic Control
Volume
60
Issue
9
Page
2291 - 2306
IST-REx-ID

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Chatterjee K, Prabhu V. Quantitative temporal simulation and refinement distances for timed systems. IEEE Transactions on Automatic Control. 2015;60(9):2291-2306. doi:10.1109/TAC.2015.2404612
Chatterjee, K., & Prabhu, V. (2015). Quantitative temporal simulation and refinement distances for timed systems. IEEE Transactions on Automatic Control, 60(9), 2291–2306. https://doi.org/10.1109/TAC.2015.2404612
Chatterjee, Krishnendu, and Vinayak Prabhu. “Quantitative Temporal Simulation and Refinement Distances for Timed Systems.” IEEE Transactions on Automatic Control 60, no. 9 (2015): 2291–2306. https://doi.org/10.1109/TAC.2015.2404612.
K. Chatterjee and V. Prabhu, “Quantitative temporal simulation and refinement distances for timed systems,” IEEE Transactions on Automatic Control, vol. 60, no. 9, pp. 2291–2306, 2015.
Chatterjee K, Prabhu V. 2015. Quantitative temporal simulation and refinement distances for timed systems. IEEE Transactions on Automatic Control. 60(9), 2291–2306.
Chatterjee, Krishnendu, and Vinayak Prabhu. “Quantitative Temporal Simulation and Refinement Distances for Timed Systems.” IEEE Transactions on Automatic Control, vol. 60, no. 9, IEEE, 2015, pp. 2291–306, doi:10.1109/TAC.2015.2404612.

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