Resetting Infinite Time Blum-Shub-Smale-Machines
Merlin Carl, Lorenzo Galeotti
Abstract:
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 ma- chines. 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].