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tracking computability of GPAC-generable functions

JOURNAL OF LOGIC AND COMPUTATION 2021年第1期31卷 326-346页

作者： Pocas, Diogo Zucker, Jeffery Univ Lisbon Fac Ciencias Dept Informat LASIGE P-1749016 Lisbon Portugal McMaster Univ Dept Comp & Software Hamilton ON L8S 4K1 Canada

Analog computation attempts to capture any type of computation, that can be realized by any type of physical system or physical process, including but not limited to computation over continuous measurable quantities. A pioneering model is the General Purpose Analog Computer (GPAC), initially presented by Shannon in 1941. The GPAC is capable of manipulating real-valued data streams;however, it has been shown to be strictly less powerful than other models of computation on the reals, such as computable analysis. In previous work, we proposed an extension of the Shannon GPAC, denoted LGPAC, designed to overcome its limitations. Not only is the LGPAC model capable of expressing computation over general data spaces X, but it also directly incorporates approximating computations by means of a limit module. An important feature of this work is the generalisation of the framework of the computation theory from Banach to Frechet spaces. In this paper, we compare the LGPAC with a digital model of computation based on effective representations (tracking computability). We establish general conditions under which LGPAC-generable functions are tracking computable.

关键词： generalized computability generalized recursion theory computation on the reals analog computation Shannon GPAC tracking computability

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tracking computability of GPAC-Generable Functions

Tracking Computability of GPAC-Generable Functions

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International Symposium on Logical Foundations of Computer Science (LFCS)

作者： Pocas, Diogo Zucker, Jeffery Tech Univ Munich Operat Res Munich Germany McMaster Univ Dept Comp & Software Hamilton ON Canada

ISBN: (纸本)9783030367558;9783030367541

Analog computation attempts to capture any type of computation, that can be realized by any type of physical system or physical process, including but not limited to computation over continuous measurable quantities. A pioneering model is the General Purpose Analog Computer (GPAC), initially presented by Shannon in 1941. The GPAC is capable of manipulating real-valued data streams;however, it has been shown to be strictly less powerful than other models of computation on the reals, such as computable analysis. In previous work, we proposed an extension of the Shannon GPAC, denoted LGPAC, designed to overcome its limitations. Not only is the LGPAC model capable of expressing computation over general data spaces X, it also directly incorporates approximating computations by means of a limit module. In this paper, we compare the LGPAC with a digital model of computation based on effective representations (tracking computability). We establish general conditions under which LGPAC-generable functions are tracking computable.

关键词： Generalized computability Generalized recursion theory Computation on the reals Analog computation Shannon GPAC tracking computability

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