Monitoring parametric temporal logic

Runtime verification techniques allow us to monitor an execution and check whether it satisfies some given property. Efficiency in runtime verification is of critical importance, because the evaluation is performed while new events are monitored. We apply runtime verification to obtain quantitative information about the execution, based on linear-time temporal properties: the temporal specification is extended to include parameters that are instantiated according to a measure obtained at runtime. The measure is updated in order to maintain the best values of parameters, according to their either maximizing or minimizing behavior, and priority. We provide measuring algorithms for linear-time temporal logic with parameters (PLTL). Our key result is that achieving efficient runtime verification is dependent on the determinization of the measuring semantics of PLTL. For deterministic PLTL, where all disjunctions are guarded by atomic propositions, online measuring requires only linear space in the size of the specification and logarithmic space in the length of the trace. For unambiguous PLTL, where general disjunctions are allowed, but the measuring is deterministic in the truth values of the non-parametric subformulas, the required space is exponential in the size of the specification, but still logarithmic in the length of the trace. For full PLTL, we show that online measuring is inherently hard and instead provide an efficient offline algorithm.