🤖 AI Summary
Existing runtime monitors support only Boolean specification verification, making it infeasible to progressively approximate quantitative properties—such as average response time—over infinite traces. Method: This paper establishes the first unified formal framework for quantitative approximate monitoring, introducing quantitative monitors whose estimates monotonically improve as observation prefixes grow, and rigorously modeling the trade-off between estimation accuracy and resource consumption (specifically, register count). Contribution/Results: We prove that register count strictly determines the theoretical upper bound on achievable accuracy; moreover, each additional register strictly increases the attainable precision—demonstrating an irreducible, non-compensatory relationship between resources and accuracy. Our framework conservatively extends classical Boolean monitoring theory while ensuring soundness. The proposed approach provides provably optimal, resource-bounded approximate monitoring for critical performance metrics, enabling verifiable, deployment-aware runtime assurance.
📝 Abstract
In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace’s unknown property value. Consequently, quantitative monitors can be compared with regard to a precision-cost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision.