1,468 research outputs found
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
Conduction States with Vanishing Dimerization in Pt Nanowires on Ge(001) Observed with Scanning Tunneling Microscopy
The low-energy electronic properties of one-dimensional nanowires formed by
Pt atoms on Ge(001) are studied with scanning tunneling microscopy down to the
millivolt-regime. The chain structure exhibits various dimerized elements at
high tunneling bias, indicative of a substrate bonding origin rather than a
charge density wave. Unexpectedly, this dimerization becomes vanishingly small
when imaging energy windows close to the Fermi level with adequately low
tunneling currents. Evenly spaced nanowire atoms emerge which are found to
represent conduction states. Implications for the metallicity of the chains are
discussed.Comment: 4 pages, 4 figure
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
Encoding monomorphic and polymorphic types
Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank-1 polymorphism and present alternative schemes that lighten
the translation of polymorphic symbols based on the novel notion of “cover”. The new encodings are implemented, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes
Pressure dependence of the Verwey transition in magnetite: an infrared spectroscopic point of view
We investigated the electronic and vibrational properties of magnetite at
temperatures from 300 K down to 10 K and for pressures up to 10 GPa by
far-infrared reflectivity measurements. The Verwey transition is manifested by
a drastic decrease of the overall reflectance and the splitting of the phonon
modes as well as the activation of additional phonon modes. In the whole
studied pressure range the down-shift of the overall reflectance spectrum
saturates and the maximum number of phonon modes is reached at a critical
temperature, which sets a lower bound for the Verwey transition temperature
T. Based on these optical results a pressure-temperature phase
diagram for magnetite is proposed.Comment: 5 pages, 4 figures; accepted for publication in J. Appl. Phy
Heat capacity of the quantum magnet TiOCl
Measurements of the heat capacity C(T,H) of the one-dimensional quantum
magnet TiOCl are presented for temperatures 2K < T < 300K and magnetic fields
up to 5T. Distinct anomalies at 91K and 67K signal two subsequent phase
transitions. The lower of these transitions clearly is of first order and seems
to be related to the spin degrees of freedom. The transition at 92K probably
involves the lattice and/or orbital moments. A detailed analysis of the data
reveals that the entropy change through both transitions is surprisingly small
(~ 0.1R), pointing to the existence strong fluctuations well into the
non-ordered high-temperature phase. No significant magnetic field dependence
was detected.Comment: 4 pages, 2 figure
Strictly One-Dimensional Electron System in Au Chains on Ge(001) Revealed By Photoelectron K-Space Mapping
Atomic nanowires formed by Au on Ge(001) are scrutinized for the band
topology of the conduction electron system by k-resolved photoemission. Two
metallic electron pockets are observed. Their Fermi surface sheets form
straight lines without undulations perpendicular to the chains within
experimental uncertainty. The electrons hence emerge as strictly confined to
one dimension. Moreover, the system is stable against a Peierls distortion down
to 10 K, lending itself for studies of the spectral function. Indications for
unusually low spectral weight at the chemical potential are discussed.Comment: 4 pages, 4 figures - revised version with added Fig. 2e) and
additional reference
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