Visibly Linear Temporal Logic

We introduce a robust and tractable temporal logic, we call Visibly Linear Temporal Logic (VLTL), which captures the full class of Visibly Pushdown Languages. The novel logic avoids fix points and provides instead natural temporal operators with simple and intuitive semantics. We prove that the complexities of the satisfiability and visibly pushdown model checking problems are the same as for other well known logics, like CaRet and the nested word temporal logic NWTL, which in contrast are strictly more limited in expressive power than VLTL. Moreover, formulas of CaRet and NWTL can be easily and inductively translated in linear-time into VLTL.