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Arjun Radhakrishna

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3 papers

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TCS Journal 2014 Journal Article

Interface simulation distances

Pavol Černý
Martin Chmelík
Thomas A. Henzinger
Arjun Radhakrishna

The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.

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GandALF Workshop 2012 Workshop Paper

Interface Simulation Distances

Pavol Černý
Martin Chmelík
Thomas A. Henzinger
Arjun Radhakrishna

The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.

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TCS Journal 2012 Journal Article

Simulation distances

Pavol Černý
Thomas A. Henzinger
Arjun Radhakrishna

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.

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