The complexity of mean payoff games on graphs
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Theoretical Computer Science
Information and Computation
Software Metrics: A Rigorous and Practical Approach
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Toward an Approximation Theory for Computerised Control
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Alternating Refinement Relations
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Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
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Approximating and computing behavioural distances in probabilistic transition systems
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Weighted automata and weighted logics
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Comparing software metrics tools
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Linear and Branching System Metrics
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An algebraic definition of simulation between programs
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Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Robust discrete synthesis against unspecified disturbances
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Defining distances for all process semantics
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Synthesis from incompatible specifications
Proceedings of the tenth ACM international conference on Embedded software
Making weighted containment feasible: a heuristic based on simulation and abstraction
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
A theory of robust omega-regular software synthesis
ACM Transactions on Embedded Computing Systems (TECS)
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Boolean notions of correctness are formalized by preorders on systems. Quantitative measures of correctness can be formalized by realvalued 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.