On the expressiveness of TPTL and MTL

TPTL and MTL are two classical timed extensions of LTL. In this paper, we prove the 20-year-old conjecture that TPTL is strictly more expressive than MTL. But we show that, surprisingly, the TPTL formula proposed by Alur and Henzinger for witnessing this conjecture it can be expressed in MTL. More generally, we show that TPTL formulae using only modality F can be translated into MTL.