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From: fernau@ira.uka.de (Henning Fernau)
Newsgroups: comp.theory
Subject: Re: do computers believe in real numbers?
Message-ID: <FERNAU.91Apr8153504@i90s7.ira.uka.de>
Date: 8 Apr 91 14:35:04 GMT
References: <7197@munnari.oz.au> <91090.154205NN1@awiwuw11.wu-wien.ac.at>
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Organization: Universitaet Karlsruhe, Karlsruhe, Deutschland.
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In-Reply-To: NN1@awiwuw11.wu-wien.ac.at's message of 1 Apr 91 19: 15:47 GMT

Well, there is lots of work on computable real numbers.
I just want to point to some more or less recent articles:

@string{bamsnew = "Bulletin of the American Mathematical Society (new series)"}
@string{fundmath = "Fundamenta Mathematicae"}

@ARTICLE{Grz55,
	AUTHOR = "A. Grzegorzyk",
	TITLE = "Computable functionals",
	JOURNAL = fundmath,
	YEAR = 1955,
	month = "",
	volume = 42,
	number = "",
	pages = "168--202",
	copy = ""
}

@ARTICLE{Grz55a,
	AUTHOR = "A. Grzegorzyk",
	TITLE = "On the definition of computable functionals",
	JOURNAL = fundmath,
	YEAR = 1955,
	month = "",
	volume = 42,
	number = "",
	pages = "232--239",
	copy = ""
}

@ARTICLE{Grz57,
	AUTHOR = "A. Grzegorzyk",
	TITLE = "On the definitions of computable real continuous functions",
	JOURNAL = fundmath,
	YEAR = 1957,
	month = "",
	volume = 44,
	number = "",
	pages = "61--71",
	copy = ""
}

@INPROCEEDINGS{BluShuSma88,
	AUTHOR = "L. Blum and M. Shub and S. Smale",
	TITLE = "On a theory of computation over the real numbers;
{NP} completeness, recursive functions and universal machines",
	BOOKTITLE = "{FOCS} proceedings",
	YEAR = 1988,
	pages = "387--397",
	organization = "{FOCS}",
	copy = ""
}

@ARTICLE{BluShuSma89,
	AUTHOR = "L. Blum and M. Shub and S. Smale",
	TITLE =  "On a theory of computation and complexity over the real numbers;
{NP} completeness, recursive functions and universal machines",
	JOURNAL = bamsnew,
	YEAR = 1989,
	volume = 21,
	number = "1",
	pages = "1--46",
	copy = ""
}

@INPROCEEDINGS{Wei89,
	AUTHOR = "K. Weihrauch",
	TITLE = "Constructivity, computability, and computational
complexity in analysis",
	BOOKTITLE = "{LNCS} 380: {FCT}",
	YEAR = 1989,
	pages = "480--493",
	organization = "{FCT}",
	copy = ""
}

Enjoy it,
 
Henning Fernau
Lehrstuhl Informatik fuer Ingenieure und Naturwissenschaftler
University of Karlsruhe
Am Fasanengarten 5
D-7500 Karlsruhe 1

phone: [West Germany](0721)608-4336
email:fernau@ira.uka.de