Parametric temporal logic for model measuring

We extend the standard model checking paradigm of linear temporal logic, LTL, to a \model measuring" paradigm where one can obtain more quantitative information beyond a "Yes/No" answer. For this purpose, we define a parametric temporal logic, PLTL, which al- lows statements such as "a request p is followed in at most x steps by a response q", where x is a free variable. We show how one can, given a formula (x₁; : : : ; x_k) of PLTL and a system model K, not only de- Termine whether there exists a valuation of x₁; : : : ; x_k under which the system K satisfies the property ', but if so find valuations which sa- Tisfy various optimality criteria. In particular, we present algorithms for finding valuations which minimize (or maximize) the maximum (or mi- nimum) of all parameters. These algorithms exhibit the same PSPACE complexity as LTL model checking.We show that our choice of syntax for PLTL lies at the threshold of decidability for parametric temporal logics, in that several natural extensions have undecidable "model measuring" problems.