  In this paper, we study strengthenings of Infinite Times
Blum-Shub-Smale-Machines (ITBMs) that were proposed by Seyfferth in [14] and
Welch in [15] obtained by modifying the behaviour of the machines at limit
stages. In particular, we study Strong Infinite Times Blum-Shub-Smale-Machines
(SITBMs), a variation of ITBMs where lim is substituted by lim inf in computing
the content of registers at limit steps. We will provide lower bounds to the
computational strength of such machines. Then, we will study the computational
strength of restrictions of SITBMs whose computations have low complexity. We
will provide an upper bound to the computational strength of these machines, in
doing so we will strenghten a result in [15] and we will give a partial answer
to a question posed by Welch in [15].
