  Timed temporal logics exhibit a bewildering diversity of operators and the
resulting decidability and expressiveness properties also vary considerably. We
study the expressive power of timed logics TPTL[U,S] and MTL[U,S] as well as of
their several fragments. Extending the LTL EF games of Etessami and Wilke, we
define MTL Ehrenfeucht-Fraisse games on a pair of timed words. Using the
associated EF theorem, we show that, expressively, the timed logics
BoundedMTL[U,S], MTL[F,P] and MITL[U,S] (respectively incorporating the
restrictions of boundedness, unary modalities and non-punctuality), are all
pairwise incomparable. As our first main result, we show that MTL[U,S] is
strictly contained within the freeze logic TPTL[U,S] for both weakly and
strictly monotonic timed words, thereby extending the result of Bouyer et al
and completing the proof of the original conjecture of Alur and Henziger from
1990. We also relate the expressiveness of a recently proposed deterministic
freeze logic TTL[X,Y] (with NP-complete satisfiability) to MTL. As our second
main result, we show by an explicit reduction that TTL[X,Y] lies strictly
within the unary, non-punctual logic MITL[F,P]. This shows that deterministic
freezing with punctuality is expressible in the non-punctual MITL[F,P].
