  There is a scalability gap between probabilistic and non-probabilistic
verification. Probabilistic model checking tools are based either on explicit
engines or on (Multi-Terminal) Binary Decision Diagrams. These structures are
complemented in areas of non-probabilistic verification by more scalable
techniques, such as IC3. We present a symbolic probabilistic model checking
algorithm based on IC3-like incremental construction of inductive clauses to
partition the state space, interleaved with incremental construction of a
system of linear inequalities. This paper compares our implementation to
standard quantitative verification alternatives: our experiments show that our
algorithm is a step to more scalable symbolic verification of rare events in
finite-state Markov chains.
