Parallel Verification of Natural Deduction Proof Graphs

Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these dependency links can determine how long it takes to verify the validity of the entire proof. Towards this end, we present a set of parallel algorithms for the formal verification of graph-based natural-deduction (ND) style proofs. We introduce a definition of layering that captures dependencies between the proof steps (nodes). Nodes in each layer can then be verified in parallel as long as prior layers have been verified. To evaluate the performance of our algorithms on proof graphs, we propose a framework for finding the performance bounds and patterns using directed acyclic network topologies (DANTs). This framework allows us to create concrete instances of DANTs for empirical evaluation of our algorithms. With this, we compare our set of parallel algorithms against a serial implementation with two experiments: one scaling both the problem size and the other scaling the number of threads. Our findings show that parallelization results in improved verification performance for certain DANT instances. We also show that our algorithms scale for certain DANT instances with respect to the number of threads.Comment: In Proceedings LFMTP 2023, arXiv:2311.0991

Absolute properties of the main-sequence eclipsing binary FM Leo

First spectroscopic and new photometric observations of the eclipsing binary FM Leo are presented. The main aims were to determine orbital and stellar parameters of two components and their evolutionary stage. First spectroscopic observations of the system were obtained with DDO and PST spectrographs. The results of the orbital solution from radial velocity curves are combined with those derived from the light-curve analysis (ASAS-3 photometry and supplementary observations of eclipses with 1 m and 0.35 m telescopes) to derive orbital and stellar parameters. JKTEBOP, Wilson-Devinney binary modelling codes and a two-dimensional cross-correlation (TODCOR) method were applied for the analysis. We find the masses to be M_1 = 1.318 $\pm$ 0.007 and M_2 = 1.287 $\pm$ 0.007 M_sun, the radii to be R_1 = 1.648 $\pm$ 0.043 and R_2 = 1.511 $\pm$ 0.049 R_sun for primary and secondary stars, respectively. The evolutionary stage of the system is briefly discussed by comparing physical parameters with current stellar evolution models. We find the components are located at the main sequence, with an age of about 3 Gyr.Comment: 5 pages, 4 figures, to appear in MNRA

Hadronic interaction of eta and eta-prime mesons with nucleons

Due to their short life-time, flavour-neutral mesons cannot be utilized as free secondary beams or targets, and therefore a study of their interaction with nucleons is not possible via direct scattering experiments. This interaction is, however, accessible via its influence on the energy dependence - and on the phase space distributions of the cross sections for reactions in which these mesons are produced. In case of the p p --> p p eta reaction the experimentally determined distributions of the differential cross sections close to the production threshold cannot be described by taking into account the S-wave proton-proton and proton-eta interaction only. Here we show that the angular distributions determined at the COSY-11 facility reveal some evidence for P-wave admixture in the proton-proton subsystem already at an excess energy as low as Q = 15.5 MeV. We also present that one can estimate the relative strength of the eta-nucleon and eta-prime-nucleon interactions by comparison of the eta and eta-prime production yield.Comment: 4 pages, 3 figures, Talk given at 16th International Conference on Particles and Nuclei (PANIC 02), Osaka, Japan, 30 Sep - 4 Oct 200

Experimental study of the eta-meson interaction with two-nucleons

By means of the COSY-11 detection system, using a stochastically cooled proton beam of the cooler synchrotron COSY and a hydrogen cluster target, we have performed a high statistics measurement of the pp --> pp eta reaction at an excess energy of Q = 15.5 MeV. The experiment was based on the four-momentum determination of both outgoing protons. This permits to identify pp --> pp eta events and to derive the complete kinematical information of the eta-p-p-system allowing for subsequent investigations of the eta-p interaction. The observed spectrum of the invariant mass of the proton-proton system deviates strongly from the phase-space distribution revealing the influence of the final-state-interaction among the outgoing particles or nontrivial features of the primary production mechanism.Comment: 6 pages, 4 figures, Talk presented at Meson 2002, 7th International Workshop on Meson Production, Properties and Interaction, Cracow, Poland, 24-28 May 200

Analysing power A(y) in the reaction p(pol.)p --> pp eta near threshold

A first measurement of the analysing power in the reaction p(pol)p --> pp eta near the production threshold has been performed at the internal facility COSY-11 at the COoler SYnchrotron COSY.Comment: 4 pages, 2 figures, Presented at Meson 2002: 7th International Workshop on Production, Properties and Interaction of Mesons, Cracow, Poland, 24-28 May 200

First close-to-threshold measurement of the analyzing power Ay in the reaction p(pol)p -> pp eta

At the internal facility COSY-11 a first measurement of the reaction p(pol)p -> pp eta near the production threshold has been performed. Results for the analysing power will be presented and a comparison with one meson exchange models will be discussed.Comment: 3 pages, 3 figures, Presented at Conference on Quarks and Nuclear Physics (QNP 2002), Julich, Germany, 9-14 Jun 200

Production of eta and eta-prime mesons via the quasi-free proton-neutron interaction

A comparison of the close-to-threshold total cross sections for the eta-prime meson production in both the pp --> pp eta-prime and pn --> pn eta-prime reactions should provide insight into the flavour-singlet (perhaps also into gluonium) content of the eta-prime meson and the relevance of quark-gluon or hadronic degrees of freedom in the creation process. The excitation function for the reaction pp --> pp eta-prime has been already established. At present, experimental investigations of the quasi-free pn --> pn X reactions are carried out at the COSY-11 facility using a beam of stochastically cooled protons and the deuteron cluster target. A method of measurement and preliminary results from the test experiments of the pn --> pn eta reaction are presented in this report.Comment: 5 pages, 5 figures, Presented at X. International Conference On Hadron Spectroscopy (Hadron 2003), Aschaffenburg, Germany, 31 Aug - 6 Sep 200

Total and Differential Cross Sections for the pp-->pp eta-prime Reaction Near Threshold

The eta-prime meson production in the reaction pp-->pp eta-prime has been studied at excess energies of Q = 26.5, 32.5 and 46.6 MeV using the internal beam facility COSY-11 at the cooler synchrotron COSY. The total cross sections as well as one angular distribution for the highest Q-value are presented. The excitation function of the near threshold data can be described by a pure s-wave phase space distribution with the inclusion of the proton-proton final state interaction and Coulomb effects. The obtained angular distribution of the eta-prime mesons is also consistent with pure s-wave production.Comment: 6 pages, 5 figures, submitted to Eur. Phys. J.

COSY-11: an experimental facility for studying meson production in free and quasi-free nucleon-nucleon collisions

The COSY-11 experimental setup is an internal facility installed at the COoler SYnchrotron COSY in Juelich. It allows to investigate meson production in free and quasi-free nucleon-nucleon collisions, eg. pp --> pp meson and pd --> p_sp np meson reactions. Drift chambers and scintillators permit to measure outgoing protons, separated in magnetic field of COSY-11 dipole. Neutrons are registered in the neutron modular detector installed downstream the beam. Recently, the experimental setup has been extended with spectator detector, deuteron drift chamber and polarization monitoring system, and since then meson production can be investigated also as a function of spin and isospin of colliding nucleons.Comment: Presented at LEAP05: International conference on Low Energy Antiproton Physics, Bonn - Juelich, Germany, May 16-22, 200