Search Results

In this paper we consider two different views of the model checking problem for the Linear Temporal Logic (LTL). On the one hand, we consider the universal model checking problem for LTL, where one asks that for a given system and a given formula all the runs of the system satisfy the formula. On the other hand, the fair model checking problem for LTL asks that for a given system and a given formula almost all the runs of the system satisfy the formula. It was shown that these two problems have the same theoretical complexity, i.e. PSPACE-complete. A less expensive fragment was identified in a previous work, namely the Muller fragment, which consists of combinations of repeated reachability properties. We consider prompt LTL formulas (pLTL), that extend LTL with an additional operator, i.e. the prompt-eventually. This operator ensures the existence of a bound such that reachability properties are satisfied within this bound. This extension comes at no cost since the model checking problem remains PSPACE-complete. We show that the corresponding Muller fragment of pLTL, with prompt repeated reachability properties, enjoys similar computational improvements. Another feature of Muller formulas is that the model checking problem becomes easier under the fairness assumption. This distinction is lost in the prompt setting, as we show that the two problems are equivalent instance-wise. Subsequently, we identify a new prefix independent fragment of pLTL for which the fair model checking problem is less expensive than the universal one.