4,982 research outputs found

    Complexity Bounds for Ordinal-Based Termination

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    `What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

    A sense of self-suspicion: global legal pluralism and the claim to legal authority

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    Legal pluralism has become common currency in many contemporary debates on law and globalization. Its main claim is that a form of global legal pluralism represents both the most accurate description of law in times of globalization and the best normative option. On the descriptive level, global legal pluralism is considered more reliable than state-based accounts. On the normative level, global legal pluralism is understood as a possibility to open up the legal realm to previously unheard voices. This article assesses these claims against the background of classic legal-pluralist scholarship. After reconstructing the emergence of global legal pluralism and then examining its epistemic and normative versions, the last two sections identify the shortcoming of this approach by underlining the absence of what the authors call ‘a sense of self-suspicion’ in drawing the map of legalities in the global sphere. The main argument put forward is that global legal pluralism is oblivious of a few key insights offered by the founding fathers of classic legal pluralism

    Splitting Sensitivity of the Ground and 7.6 eV Isomeric States of 229Th

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    The lowest-known excited state in nuclei is the 7.6 eV isomer of 229Th. This energy is within the range of laser-based investigations that could allow accurate measurements of possible temporal variation of this energy splitting. This in turn could probe temporal variation of the fine-structure constant or other parameters in the nuclear Hamiltonian. We investigate the sensitivity of this transition energy to these quantities. We find that the two states are predicted to have identical deformations and thus the same Coulomb energies within the accuracy of the model (viz., within roughly 30 keV). We therefore find no enhanced sensitivity to variation of the fine-structure constant. In the case of the strong interaction the energy splitting is found to have a complicated dependence on several parameters of the interaction, which makes an accurate prediction of sensitivity to temporal changes of fundamental constants problematical. Neither the strong- nor Coulomb-interaction contributions to the energy splitting of this doublet can be constrained within an accuracy better than a few tens of keV, so that only upper limits can be set on the possible sensitivity to temporal variations of the fundamental constants.Comment: 4 pages, 2 figure

    Minimal Mass Matrices for Dirac Neutrinos

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    We consider the possibility of neutrinos being Dirac particles and study minimal mass matrices with as much zero entries as possible. We find that up to 5 zero entries are allowed. Those matrices predict one vanishing mass state, CP conservation and U_{e3} either zero or proportional to R, where R is the ratio of the solar and atmospheric \Delta m^2. Matrices containing 4 zeros can be classified in categories predicting U_{e3} = 0, U_{e3} \neq 0 but no CP violation or |U_{e3}| \neq 0 and possible CP violation. Some cases allow to set constraints on the neutrino masses. The characteristic value of U_{e3} capable of distinguishing some of the cases with non-trivial phenomenological consequences is about R/2 \sin 2 \theta_{12}. Matrices containing 3 and less zero entries imply (with a few exceptions) no correlation for the observables. We outline models leading to the textures based on the Froggatt-Nielsen mechanism or the non-Abelian discrete symmetry D_4 \times Z_2.Comment: 32 pages, 3 figures. Comments and references added. To appear in JHE

    Epimorphisms between linear orders

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    We study the relation on linear orders induced by order preserving surjections. In particular we show that its restriction to countable orders is a bqo.Comment: 15 pages; in version 2 we corrected some typos and rewrote the paragraphs introducing the results of subsection 3.3 (statements and proofs are unchanged
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