Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Approximate Simulation Relations for Hybrid Systems
Discrete Event Dynamic Systems
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IEEE Transactions on Software Engineering
An intrinsic characterization of approximate probabilistic bisimilarity
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Z-reachability problem for games on 2-dimensional vector addition systems with states is in P
RP'10 Proceedings of the 4th international conference on Reachability problems
Church synthesis problem for noisy input
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Crossing the bridge between similar games
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
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ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
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FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Continuity and robustness of programs
Communications of the ACM
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We introduce quantatitive timed refinement metrics and quantitative timed simulation functions, incorporating zenoness checks, for timed systems. These functions assign positive real numbers between zero and infinity which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximum timing mismatch that can arise, (2) the "steady-state" maximum timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation functions to within any desired degree of accuracy. In order to compute the values of the quantitative simulation functions, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives for player 1, and then use these algorithms to compute the values of the quantitative timed simulation functions.