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Infinite Oracle Queries in Type-2 Machines (Extended Abstract) (0907.3230v1)
Published 20 Jul 2009 in cs.LO
Abstract: We define Oracle-Type-2-Machine capable of writing infinite oracle queries. In contrast to finite oracle queries, this extends the realm of oracle-computable functions into the discontinuous realm. Our definition is conservative; access to a computable oracle does not increase the computational power. Other models of real hypercomputation such as Ziegler's (finitely) revising computation or Type-2-Nondeterminism are shown to be special cases of Oracle-Type-2-Machines. Our approach offers an intuitive definition of the weakest machine model capable to simulate both Type-2-Machines and BSS machines.