Better Space Bounds for Future-Looking Stream Monitors

The LogicGuard specification language for the runtime monitoring of event steams represents monitors as predicate logic formulas of a certain kind. In this paper we derive upper bounds for the runtime representation size of a LogicGuard monitor specification under the assumption that in these formulas quantifiers can be arbitrarily nested, but in the body of each quantifier there is at most one quantifier. Such monitors can be described by quantifier vectors. We provide an analytic expression for the runtime representation size of an important class of the monitors which we represent by standard evaluation vectors. Based on this optimal solution, we provide a method for computing the runtime representation size of a monitor, which proceeds by manipulation of the intervals of quantifier bounds. We show that this method gives a good approximation of the optimal solution for the general class and always outperforms results for the runtime representation size presented earlier.