  The problem of verifying the "Unbounded Until" fragment in temporal logic
formulas has been studied extensively in the past, especially in the context of
statistical model checking. Statistical model checking, a computationally
inexpensive sampling based alternative to the more expensive numerical model
checking technique, presents the following decision dilemma -- what length of
the sample is enough in general? In this paper, we discuss an algorithm for
this problem that combines ideas from graph theory, statistical model checking
and numerical model checking. We analyze the algorithm and show through
experiments that this approach outperforms the standard statistical model
checking algorithm for verifying unbounded until for low density Discrete Time
Markov Chains.
