This paper is concerned with the verification of finite Markov chains against
parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with
a bound that contains variables; e.g., ◊≤x​ φ asserts that
φ holds within x time steps, where x is a variable on natural
numbers. The central problem studied in this paper is to determine the set of
parameter valuations V≺p​(φ) for which the probability to
satisfy pLTL-formula φ in a Markov chain meets a given threshold ≺p, where ≺ is a comparison on reals and p a probability. As for pLTL
determining the emptiness of V>0​(φ) is undecidable, we consider
several logic fragments. We consider parametric reachability properties, a
sub-logic of pLTL restricted to next and ◊≤x​, parametric B\"uchi
properties and finally, a maximal subclass of pLTL for which emptiness of V>0​(φ) is decidable.Comment: TCS Track B 201