Boolean notions of correctness are formalized by preorders on systems. Quantitative measures of correctness can be formalized by real-valued distance functions between systems, where the distance between implementation and specification provides a measure of “fit” or “desirability.” We extend the simulation preorder to the quantitative setting, by making each player of a simulation game pay a certain price for her choices. We use the resulting games with quantitative objectives to define three different simulation distances. The correctness distance measures how much the specification must be changed in order to be satisfied by the implementation. The coverage distance measures how much the implementation restricts the degrees of freedom offered by the specification. The robustness distance measures how much a system can deviate from the implementation description without violating the specification. We consider these distances for safety as well as liveness specifications. The distances can be computed in polynomial time for safety specifications, and for liveness specifications given by weak fairness constraints. We show that the distance functions satisfy the triangle inequality, that the distance between two systems does not increase under parallel composition with a third system, and that the distance between two systems can be bounded from above and below by distances between abstractions of the two systems. These properties suggest that our simulation distances provide an appropriate basis for a quantitative theory of discrete systems. We also demonstrate how the robustness distance can be used to measure how many transmission errors are tolerated by error correcting codes.
This work was partially supported by the European Union project COMBEST and the European Network of Excellence ArtistDesign.
235 - 268
CONCUR: Concurrency Theory
2010-08-31 – 2010-09-03
Cerny P, Henzinger TA, Radhakrishna A. Simulation distances. In: Vol 6269. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2010:235-268. doi:10.1007/978-3-642-15375-4_18
Cerny, P., Henzinger, T. A., & Radhakrishna, A. (2010). Simulation distances (Vol. 6269, pp. 235–268). Presented at the CONCUR: Concurrency Theory, Paris, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.1007/978-3-642-15375-4_18
Cerny, Pavol, Thomas A Henzinger, and Arjun Radhakrishna. “Simulation Distances,” 6269:235–68. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010. https://doi.org/10.1007/978-3-642-15375-4_18.
P. Cerny, T. A. Henzinger, and A. Radhakrishna, “Simulation distances,” presented at the CONCUR: Concurrency Theory, Paris, France, 2010, vol. 6269, pp. 235–268.
Cerny P, Henzinger TA, Radhakrishna A. 2010. Simulation distances. CONCUR: Concurrency Theory, LNCS, vol. 6269. 235–268.
Cerny, Pavol, et al. Simulation Distances. Vol. 6269, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010, pp. 235–68, doi:10.1007/978-3-642-15375-4_18.