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.

Enhanced Thermal Shock Resistance of Ceramics through Biomimetically Inspired Nanofins

We propose here a new method to make ceramics insensitive to thermal shock up to their melting temperature. In this method the surface of ceramics was biomimetically roughened into nanofinned surface that creates a thin air layer enveloping the surface of the ceramics during quenching. This air layer increases the heat transfer resistance of the surface of the ceramics by about 10 000 times so that the strong thermal gradient and stresses produced by the steep temperature difference in thermal shock did not occur both on the actual surface and in the interior of the ceramics. This method effectively extends the applications of existing ceramics in the extreme thermal environments.