2004
DOI: 10.1016/j.jco.2004.06.001
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Abstract: In the last years, recursive functions over the reals (Theoret. Comput. Sci. 162 (1996) 23) have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes (Unconventional Models of Computation, UMC 2002, minimalization operator, has not been considered: (a) although differential recursion (the analog counterpart of classical recurrence) is, in some extent, directly implementable in the General Purpose Analog Computer of… Show more

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Cited by 32 publications
(49 citation statements)
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“…For example, it may be interesting to work out Mycka and Costa's class arising from the operator of taking limits [14].…”
Section: Open Problemsmentioning
confidence: 99%
“…For example, it may be interesting to work out Mycka and Costa's class arising from the operator of taking limits [14].…”
Section: Open Problemsmentioning
confidence: 99%
“…The sets of those real functions 54 can be definable by a general-purpose analog computer 57 or GPAC, which is a general computing model evolving in continuos time l . Then even if weights and spikes are restricted to Turing-computable functions, the brain neural network might be not closed if at least an operation is not recursive possibly (see 15 16 The class of R-recursive functions is very large. It contains many traditionally non-computable functions, such as the characteristic functions of sets of the arithmetical hierarchy 42,45 .…”
Section: Other Sources Of Computational Power: Spikes and Operationsmentioning
confidence: 99%
“…Similarly, one can define generability via approximations for PGPACs, F-ICs, etc. It is also worthwhile to remark that, due to the connections between PGPAC-computable functions and R-recursive functions presented in [11], if f is generated by a PGPAC via approximations, then f belongs to the class H 1 presented in [20]. 7 Moreover, f is also computable by Rubel's Extended Analog Computer [29].…”
Section: Outputmentioning
confidence: 99%