Probabilistic Solutions to Merchant Problems: Locating of the False Stack

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dc.contributor.author Oleinik, V.L. en
dc.contributor.author Pavlov, B. en
dc.date.accessioned 2009-08-28T03:22:18Z en
dc.date.available 2009-08-28T03:22:18Z en
dc.date.issued 2004-12 en
dc.identifier.citation Department of Mathematics - Research Reports-533 (2004) en
dc.identifier.issn 1173-0889 en
dc.identifier.uri http://hdl.handle.net/2292/5090 en
dc.description.abstract In [1] a probabilistic solution to the Infinite Merchant's Problem, an undecidable problem equivalent to the Halting Problem, was proposed. The solution uses a real Hilbert space and is based on the estimation of the exponential growth of an unbounded semigroup. In [2] was offered an alternative solution in terms of scattering processes on quantum dots. The authors reduced the problem to a special scattering problem and testify the "halting phenomenon" based on the quantum measurement of results of scattering with random input data. The a-posteriori probability of halting, subject to the negative results of multiple independent tests, was estimated. The possibility of location the number of the bag with false coins in finite-dimensional case was noticed in [1] and proved in [2]. The aim of this paper is to offer a solution of the latter problem in the infinite case. [1] C.S. Calude, B.S. Pavlov. Coins, quantum measurements, and Turing's barrier, Quantum Information Processing, 1, 1--2 (2002), 107--127. [2] V.A. Adamyan, C.S. Calude, B.S. Pavlov, A quantum scattering approach to undecidable problem. In: Quantum information and complexity, Proceedings of the Meijo Winter School 2003, Meijo University, Nagoya, Japan, 6 - 10 January 2003, edited by T Hida, K Saitô (Meijo University, Japan) and Si Si (Aichi Prefectural University, Japan). en
dc.publisher Department of Mathematics, The University of Auckland, New Zealand en
dc.relation.ispartofseries Research Reports - Department of Mathematics en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri http://www.math.auckland.ac.nz/Research/Reports/view.php?id=533 en
dc.title Probabilistic Solutions to Merchant Problems: Locating of the False Stack en
dc.type Technical Report en
dc.subject.marsden Fields of Research::230000 Mathematical Sciences::230100 Mathematics en
dc.rights.holder The author(s) en


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