automatic construction of finite algebras

This paper deals withmodel generation for equational theories, i.e., automatically generating (finite) models of a given set of (logical) equations. Our method of finite model generation and a tool for automatic construction of finite algebras is described. Some examples are given to show the applications of our program. We argue that, the combination of model generators and theorem provers enables us to get a better understanding of logical theories. A brief comparison between our tool and other similar tools is also presented.

constructing finite algebras with falcon

The generation of models and counterexamples is an important form of reasoning. In this paper, we give a formal account of a system, called FALCON, for constructing finite algebras from given equational axioms. The abstract algorithms, as well as some implementation details and sample applications, are presented. The generation of finite models is viewed as a constraint satisfaction problem, with ground instances of the axioms as constraints. One feature of the system is that it employs a very simple technique, called the least number heuristic, to eliminate isomorphic (partial) models, thus reducing the size of the search space. The correctness of the heuristic is proved. Some experimental data are given to show the performance and applications of the system.

Probing the Structure of Unstable Nuclei Through the Recoiled Proton Tagged Knockout Reaction

Recoiled proton tagged knockout reaction experiments were carried-out for He-8 at 82.5 MeV/u in RIKEN and for He-6 at 65 MeV/u in Lanzhou. The very preliminary results for the distinguish of the reaction mechanism are presented and compared to the kinematics calculation.

Elastic Scattering of He-6 + p at 82.3 MeV/nucleon

Differential cross sections for the elastic scattering of halo nucleus He-6 on proton target were measured at 82.3 MeV/u. The experimental results are well reproduced by optical model calculations using global potential KD02 with a reduction of the depth of real volume part by a factor of 0.7. A systematic analysis shows that this behavior might be related to the weakly bound property of unstable nuclei.

EXPERIMENTAL INVESTIGATION OF THE STELLAR REACTION S-30(p, gamma)(31) Cl VIA COULOMB DISSOCIATION

The Coulomb dissociation of the proton-rich nuclei Cl-31 was studied experimentally using Cl-31 beams at 58 MeV/nucleon with a lead target. The relative energy between the reaction products, S-30 and proton, was obtained. The first excited state in Cl-31 was observed which is relevant to the resonant capture of stellar S-30(p, gamma)Cl-31 reaction

MEASUREMENT OF TWO-PROTON CORRELATION FROM THE BREAK-UP OF Al-23

Experiments of Al-23 and Mg-22 radioactive beams bombarding a C-12 target at an energy of 60 similar to 70 A MeV have been performed at the projectile fragment separator beamline (RIPS) in the RIKEN Ring Cyclotron Facility to study the two-proton emission from Al-23 and Mg-22 excited states, respectively. The trajectorie of the decay products, namely Na-21 + p + p from Al-23 and Ne-20 + p + p from Mg-22, are clean identified. The relative momentum and opening angle between two protons in the rest frame of three body decay channels are obtained by relativistic-kinematics reconstruction. The results demonstrate that there are some di-proton emission components from He-2 cluster for the excited Al-23 and Mg-22.

MEASUREMENT OF THE PROTON-PROTON CORRELATION FUNCTION FROM THE BREAK-UP OF Mg-22 AND Ne-20

An experiment of Mg-22 and Ne-20 beams bombarding on a C-12 target at an energy of 60 similar to 70 A MeV has been performed at the RIKEN projectile fragment separator (RIPS)in the RIKEN Ring Cyclotron Facility to study the two-proton correlated emission from Mg-22 and Ne-20 excited states. The two-protons momentum correlation functions have been obtained for Mg-22 and Ne-20, respectively. The trajectories of the Mg-22 decayed products (Ne-20 + p + p) were also measured to get the angular correlations between the two protons in Center of Mass of decaying system by relativistic-kinematics reconstruction. The results exhibit that Mg-22 has the features of He-2 cluster decay mechanism.