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Quantum Computing: A new Paradigm and it's Type Theory
 Lecture given at the Quantum Computing Seminar, Lehrstuhl Prof. Beth, Universität
, 1996
"... To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization proble ..."
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To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization problem, to a quadratic complexity if quantum computed. In the paper a short introduction to quantum mechanics can be found in the appendix. With this material the operation of the quantum computer, and the ideas of quantum logic will be explained. The focus will be the argument that a connection of quantum logic and linear logic is the right type theory for quantum computing. These ideas are inspired by Vaughan Pratt's view that the intuitionistic formulas argue about states (i.e physical quantum states) and linear formulas argue about state transformations (i.e computation steps). 1 Introduction A calculus for programs on quantum computers is strongly missed. Here we present the material t...
New Connections between Mathematics and Computer Science
, 1996
"... A workshop on "New Connections between Mathematics and Computer Science" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England from 2024 November 1995. The workshop was supported by the Engineering and Physical Science Research Council of the United Kingdo ..."
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A workshop on "New Connections between Mathematics and Computer Science" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England from 2024 November 1995. The workshop was supported by the Engineering and Physical Science Research Council of the United Kingdom, the London Mathematical Society and HewlettPackard's Basic Research Institute in the Mathematical Sciences. This document contains a report on the workshop, the abstracts of the talks and the accompanying bibliography.
Extending TNorms Beyond [0,1]: Relevant Results of Semigroup Theory
, 1999
"... Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval [0, 1]; it is therefore necessary to descri ..."
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Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval [0, 1]; it is therefore necessary to describe possible extension of tnorms and tconorms to such new values. It is reasonable to require that this extension be associative, i.e., that the set of truth value with the corresponding operation form a semigroup. Semigroups have been extensively studied in mathematics. In this short paper, we describe several results from semigroup theory which we believe to be relevant for the proposed extension of tnorms and tconorms.
Internal Accession Date Only New Connections between Mathematics and Computer Science: report, abstracts and bibliography of a workshop
, 1996
"... dynamics; algorithms; algebraic topology; linear logic; complexity theory A workshop on "New Connections between Mathematics and Computer Science " was held at ..."
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dynamics; algorithms; algebraic topology; linear logic; complexity theory A workshop on "New Connections between Mathematics and Computer Science " was held at