Lee, T 2003, 'Arithmetical definability over finite structures', Mathematical Logic Quarterly, vol. 49, no. 4, pp. 385-392.
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AbstractArithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform AC0and FO(PLUS, TIMES). We prove finite analogs of three classic results in arithmetical definability, namely that < and TIMES can first‐order define PLUS, that < and DIVIDES can first‐order define TIMES, and that < and COPRIME can first‐order define TIMES. The first result sharpens the equivalence FO(PLUS, TIMES) =FO(BIT) to FO(<, TIMES) = FO(BIT), answering a question raised by Barrington et al. about the Crane Beach Conjecture. Together with previous results on the Crane Beach Conjecture, our results imply that FO(PLUS) is strictly less expressive than FO(<, TIMES) = FO(<, DIVIDES) = FO(<,COPRIME). In more colorful language, one could say that, for parallel computation, multiplication is harder than addition.
Li, S & Luo, M 2003, 'A negative answer to T. Kubiak's question', Fuzzy Sets and Systems, vol. 133, no. 3, pp. 407-409.
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T. Kubiak raised in 1992 a question about Hausdorffness and compactness in L-topology. It is negatively solved in the present paper by constructing certain L-Hausdorffness and L-compactness axioms. (C) 2002 Elsevier Science B.V. All rights reserved.
Li, S & Luo, M 2003, 'FNS is not isomorphic to FTS', Fuzzy Sets and Systems, vol. 136, no. 1, pp. 127-131.
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In this paper, we show that there are exactly c different simultaneously bireffective and bicoreflective subconstructs of FNS, in fact there exists a one-to-one correspondence between those subconstructs of FNS and open sets of (0,1). We also prove that
Li, S & Luo, M 2003, 'Generalized Lowen functors', Fuzzy Sets and Systems, vol. 133, no. 3, pp. 375-387.
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According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly important and necessary. Lowen was one of the first authors who had studied the relation between the category
Li, S & Zhang, D 2003, 'A Non-topologically Generated Hutton-lowen Uniformizable Space', Quaestiones Mathematicae, vol. 26, no. 4, pp. 471-477.
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In this note, it is shown that there exist non-topologically generated spaces which are both Lowen uniformizable and Hutton uniformizable. On the other hand, the FNS-coreflection of the Hutton unit interval I(I) is neither Lowen uniformizable nor Hutton uniformizable.
Li, SJ & Ying, MS 2003, 'Extensionality of the RCC8 composition table', FUNDAMENTA INFORMATICAE, vol. 55, no. 3-4, pp. 363-385.
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This paper is mainly concerned with the RCC8 composition table entailed by the Region Connection Calculus (RCC), a well-known formalism for Qualitative Spatial Reasoning. This table has been independently generated by Egenhofer in the context of Geograph
Li, SJ & Ying, MS 2003, 'Region Connection Calculus: Its models and composition table', ARTIFICIAL INTELLIGENCE, vol. 145, no. 1-2, pp. 121-146.
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Originating in Allen's analysis of temporal relations, the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence. This paper is mainly about the consistency-based composition table (RCC8 CT) of the Region Connection Calculus (RCC) raised by Randell, Cui and Cohn. First we show each RCC model is a consistent model of the RCC8 CT. Then after an exhaustive analysis we show that no RCC model can be interpreted extensionally anyway and hence give a negative answer to a conjecture raised by Bennett. All these results are given in an `extensional RCC8 composition table, where we attach to each cell entry in the RCC8 CT a superscript to indicate in what circumstances an extensional interpretation is possible.
Nielsen, MA, Dawson, CM, Dodd, JL, Gilchrist, A, Mortimer, D, Osborne, TJ, Bremner, MJ, Harrow, AW & Hines, A 2003, 'Quantum dynamics as a physical resource', PHYSICAL REVIEW A, vol. 67, no. 5.
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Nielsen, MA, Dawson, CM, Dodd, JL, Gilchrist, A, Mortimer, D, Osborne, TJ, Bremner, MJ, Harrow, AW & Hines, A 2003, 'Quantum dynamics as a physical resource', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 67, no. 5, pp. 523011-5230119.
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White, AG, Gilchrist, A, Pryde, GJ, O'Brien, JL, Bremner, MJ & Langford, NK 2003, 'Measuring Controlled-NOT and two-qubit gate operation', J.Opt.Soc.Am.B, vol. 24, no. 2, pp. 172-183.
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Accurate characterisation of two-qubit gates will be critical for anyrealisation of quantum computation. We discuss a range of measurements aimed atcharacterising a two-qubit gate, specifically the CNOT gate. These measurementsare architecture-independent, and range from simple truth table measurements,to single figure measures such as the fringe visibility, parity, fidelity, andentanglement witnesses, through to whole-state and whole-gate measures achievedrespectively via quantum state and process tomography. In doing so, we examinecritical differences between classical and quantum gate operation.
Ying, MS 2003, 'Reasoning about probabilistic sequential programs in a probabilistic logic', ACTA INFORMATICA, vol. 39, no. 5, pp. 315-389.
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We introduce a notion of strong monotonicity of probabilistic predicate transformers. This notion enables us to establish a normal form theorem for monotone probabilistic predicate transformers. Three other healthiness conditions, namely, conjunctivity,
OBrien, JL, Pryde, GJ, White, AG, Ralph, TC, Bell, TB, Langford, NK & Milburn, GJ 1970, 'Construction of a non-deterministic 2-photon CNOT gate', Optics InfoBase Conference Papers.
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We present progress towards construction of an optical CNOT gate. The gate is predicted to p erform all quantum gate op erations within the standard coincidence basis paradigm and test the principles of linear optical quantum computation.
O'Brien, JL, Pryde, GJ, White, AG, Ralph, TC, Bell, TB, Langford, NK & Milburn, GJ 1970, 'Construction of a non-deterministic 2-photon CNOT gate', Conference on Quantum Electronics and Laser Science (QELS) - Technical Digest Series.
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The building blocks of the two-photon CNOT were demonstrated. In particular, extensive studies to maximize the brightness and mode quality of downconversion sources and coupling of these photons into single mode fibers have enabled to investigate the high-visibility non-classical interference effects central to the successful operation of the gate. This paper investigates on simple quantum algorithms and describes a simple technique for increasing the detection efficiency of th single photon counting modules.
Pryde, GJ, O'Brien, JL, Bell, TB, Langford, NK, Milburn, GJ, Ralph, TC & White, AG 1970, 'Efficient linear optical quantum computation', QUANTUM COMMUNICATION, MEASUREMENT AND COMPUTING, PROCEEDINGS, 6th International Conference on Quantum Communication, Measurement and Computing (QCMC 02), RINTON PRESS, INC, MA, MIT, CAMBRIDGE, pp. 253-256.
Pryde, GJ, O'Brien, JL, White, AG, Ralph, TC, Bell, TB, Langford, NK & Milburn, GJ 1970, 'Experimental linear optics controlled-NOT gates', 2003 European Quantum Electronics Conference. EQEC 2003 (IEEE Cat No.03TH8665), 2003 European Quantum Electronics Conference. EQEC 2003 (IEEE Cat No.03TH8665), IEEE, pp. 385-385.
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Elements of the coincidence-CNOT (controlled-NOT) are experimentally demonstrated, which includes a bright photon source with good spatial mode quality; nonclassical interferometry; improved photon detection; and tomographic analysis. The logical circuit of the coincidence-CNOT is described in the paper.
