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Learning via queries in [+, <]

Published online by Cambridge University Press:  12 March 2014

William I. Gasarch ,
Mark G. Pleszkoch  and
Robert Solovay
William I. Gasarch
Affiliation:
Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, E-mail: pleszkoc@cs.umd.edu Department of Computer Science, University of Maryland, College Park, Maryland 20742, E-mail: markp@betasvm2.vnet.ibm.com
Mark G. Pleszkoch
Affiliation:
Department of Computer Science, University of Maryland, College Park, Maryland 20742, E-mail: markp@betasvm2.vnet.ibm.com Application Solutions Division, IBM Corporation Gaithersburg, Maryland 20877
Robert Solovay
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720, E-mail: solovay@math.berkeley.edu
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Abstract

We prove that the set of all recursive functions cannot be inferred using first-order queries in the query language containing extra symbols [+ , <]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+, <]. Additionally, we resolve an open question in [7] about passive versus active learning.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 1 , March 1992 , pp. 53 - 81
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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