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We study two unary fragments of the well-known metric interval temporal logicMITL[U_I,S_I] that was originally proposed by Alur and Henzinger, and we pindown their expressiveness as well as satisfaction complexities. We show thatMITL[F_\inf,P_\inf] which has unary modalities with only lower-boundconstraints is (surprisingly) expressively complete for Partially Ordered 2-WayDeterministic Timed Automata (po2DTA) and the reduction from logic to automatongives us its NP-complete satisfiability. We also show that the fragmentMITL[F_b,P_b] having unary modalities with only bounded intervals has\nexptime-complete satisfiability. But strangely, MITL[F_b,P_b] is strictlyless expressive than MITL[F_\inf,P_\inf]. We provide a comprehensive picture ofthe decidability and expressiveness of various unary fragments of MITL.

The Unary Fragments of Metric Interval Temporal Logic: Bounded versus Lower bound Constraints (Full Version)