Simulation distances Journal Article


Author(s): Cerný, Pavol; Henzinger, Thomas A; Radhakrishna, Arjun
Article Title: Simulation distances
Affiliation IST Austria
Abstract: 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.
Keywords: simulation; liveness; Quantitative Analysis; games; discrete systems; Distance functions; Distance measure; Error correcting code; Fairness constraints; Parallel composition; Polynomial-time; Preorders; Quantitative measures; Quantitative objectives; Quantitative theory; Safety specifications; Simulation games; Simulation preorder; Transmission error; Triangle inequality
Journal Title: Theoretical Computer Science
Volume: 413
Issue 1
ISSN: 0304-3975
Publisher: Elsevier  
Date Published: 2012-01-06
Start Page: 21
End Page: 35
Sponsor: This work was partially supported by the ERC Advanced Grant QUAREM, the FWF NFN Grant S11402-N23 (RiSE), the European Union project COMBEST and the European Network of Excellence Artist Design.
URL:
DOI: 10.1016/j.tcs.2011.08.002
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
  2. Pavol Černý
    25 Cerný
Related IST Austria Work