“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
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We investigate OREX, a temporal logic for specifying open systems. Path properties in OREX are expressed using ω-regular expressions, while similar logics for open systems, such as ATL* of Alur et al., use LTL for this purpose. Our results indicate that this distinction is an important one. In particular, we show that OREX has a more efficient model-checking procedure than ATL*, even though it is strictly more expressive. To this end, we present a single-exponential model-checking algorithm for OREX; the model-checking problem for ATL* in contrast is provably double-exponential.