Inevitability properties in branching temporal logics are of the syntax forall eventually , where is an arbitrary (timed) CTL formula. In the sense that "good things will happen", they are parallel to the "liveness" properties in linear temporal logics. Such inevitability properties in dense-time logics can be analyzed with greatest fixpoint calculation. We present algorithms to model-check inevitability properties both with and without requirement of non-Zeno computations. We discuss a technique for early decision on greatest fixpoints in the temporal logics, and experiment with the effect of non-Zeno computations on the evaluation of greatest fixpoints. We also discuss the TCTL subclass with only universal path quantifiers which allows for the safe abstraction analysis of inevitability properties. Finally, we report our implementation and experiments to show the plausibility of our ideas.
In @cite_32 , proposed an efficient symbolic model-checking algorithm for TCTL. However, the algorithm does not distinguish between Zeno and non-Zeno computations. Instead, the authors proposed to modify TAs with Zeno computations to ones without. In comparison, our greatest fixpoint evaluation algorithm is innately able to quantify over non-Zeno computations.
@cite_32
2167668895
Finite-state programs over real-numbered time in a guarded-command language with real-valued clocks are described. Model checking answers the question of which states of a real-time program satisfy a branching-time specification. An algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space, is given. >