10.15479/AT:IST-2010-0003
Cerny, Pavol
Pavol
Cerny
Henzinger, Thomas A
Thomas A
Henzinger0000−0002−2985−7724
Radhakrishna, Arjun
Arjun
Radhakrishna
Simulation distances
IST Austria Technical Report
IST Austria
2010
2018-12-12T11:39:03Z
2019-08-02T12:38:43Z
technical_report
https://research-explorer.app.ist.ac.at/record/5389
https://research-explorer.app.ist.ac.at/record/5389.json
2664-1690
367246 bytes
application/pdf
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 im- plementation 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.