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The model-checking problem for probabilistic systems crucially relies on thetranslation of LTL to deterministic Rabin automata (DRW). Our recent Safralesstranslation for the LTL(F,G) fragment produces smaller automata as compared tothe traditional approach. In this work, instead of DRW we considerdeterministic automata with acceptance condition given as disjunction ofgeneralized Rabin pairs (DGRW). The Safraless translation of LTL(F,G) formulasto DGRW results in smaller automata as compared to DRW. We present algorithmsfor probabilistic model-checking as well as game solving for DGRW conditions.Our new algorithms lead to improvement both in terms of theoretical bounds aswell as practical evaluation. We compare PRISM with and without our newtranslation, and show that the new translation leads to significantimprovements.

Automata with Generalized Rabin Pairs for Probabilistic Model Checking and LTL Synthesis