PP-2020-01: Resetting Infinite Time Blum-Shub-Smale-Machines

PP-2020-01: Carl, Merlin and Galeotti, Lorenzo (2020) Resetting Infinite Time Blum-Shub-Smale-Machines. [Pre-print] (Submitted)

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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].

Item Type: Pre-print
Report Nr: PP-2020-01
Series Name: Prepublication (PP) Series
Year: 2020
Subjects: Computation
Depositing User: lgaleot1
Date Deposited: 25 Jan 2020 19:08
Last Modified: 14 Feb 2020 13:59
URI: https://eprints.illc.uva.nl/id/eprint/1727

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