Deterministic Automata for the (F,G)-fragment of LTL

Abstract: When dealing with linear temporal logic properties in the setting of e.g. games or probabilistic systems, one often needs to express them as deterministic omega-automata. In order to translate LTL to deterministic omega-automata, the traditional approach first translates the formula to a non-deterministic B\"uchi automaton. Then a determinization procedure such as of Safra is performed yielding a deterministic \omega-automaton. We present a direct translation of the (F,G)-fragment of LTL into deterministic \omega-automata with no determinization procedure involved. Since our approach is tailored to LTL, we often avoid the typically unnecessarily large blowup caused by general determinization algorithms. We investigate the complexity of this translation and provide experimental results and compare them to the traditional method.