  We introduce a new fragment of Linear temporal logic (LTL) called LIO and a
new class of Buechi automata (BA) called Almost linear Buechi automata (ALBA).
We provide effective translations between LIO and ALBA showing that the two
formalisms are expressively equivalent. While standard translations of LTL into
BA use some intermediate formalisms, the presented translation of LIO into ALBA
is direct. As we expect applications of ALBA in model checking, we compare the
expressiveness of ALBA with other classes of Buechi automata studied in this
context and we indicate possible applications.
