Linear and Branching System Metrics
CALIFORNIA UNIV SANTA CRUZ
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We extend the basic system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances, and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and micron-calculus. We show that, while trace inclusion resp. equivalence coincides with simulation resp. bisimulation for deterministic boolean transition systems, linear and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithm. for computing the distances over finite systems, together with matching lower complexity bounds.
- Theoretical Mathematics
- Statistics and Probability