  Extended Bounded Response LTL with Past (LTLEBR+P) is a safety fragment of
Linear Temporal Logic with Past (LTL+P) that has been recently introduced in
the context of reactive synthesis. The strength of LTLEBR+P is a fully symbolic
compilation of formulas into symbolic deterministic automata. Its syntax is
organized in four levels. The first three levels feature (a particular
combination of) future temporal modalities, the last one admits only past
temporal operators. At the base of such a structuring there are algorithmic
motivations: each level corresponds to a step of the algorithm for the
automaton construction. The complex syntax of LTLEBR+P made it difficult to
precisely characterize its expressive power, and to compare it with other LTL+P
safety fragments.
  In this paper, we first prove that LTLEBR+P is expressively complete with
respect to the safety fragment of LTL+P, that is, any safety language definable
in LTL+P can be formalized in LTLEBR+P, and vice versa. From this, it follows
that LTLEBR+P and Safety-LTL are expressively equivalent. Then, we show that
past modalities play an essential role in LTLEBR+P: we prove that the future
fragment of LTLEBR+P is strictly less expressive than full LTLEBR+P.
