  This work considers weak deterministic B\"uchi automata reading encodings of
non-negative $d$-vectors of reals in a fixed base. A saturated language is a
language which contains all encoding of elements belonging to a set of
$d$-vectors of reals. A Real Vector Automaton is an automaton which recognizes
a saturated language. It is explained how to decide in quasi-linear time
whether a minimal weak deterministic B\"uchi automaton is a Real Vector
Automaton. The problem is solved both for the two standard encodings of vectors
of numbers: the sequential encoding and the parallel encoding. This algorithm
runs in linear time for minimal weak B\"uchi automata accepting set of reals.
Finally, the same problem is also solved for parallel encoding of automata
reading vectors of relative reals.
