Finding p-indecomposable Functions: FCA Approach
نویسنده
چکیده
The parametric expressibility of functions is a generalization of the expressibility via composition. All parametrically closed classes of functions (p-clones) form a lattice. For finite domains the lattice is shown to be finite, however straight-forward iteration over all functions is infeasible, and so far the p-indecomposable functions are only known for domains with two and three elements. In this work we show how pindecomposable functions can be computed more efficiently by means of an extended version of attribute exploration (AE). Due to the growing number of attributes standard AE is not able to guarantee the discovery of all p-indecomposable functions. We introduce an extension of AE and investigate its properties. We investigate the conditions allowing us to guarantee the success of exploration. In experiments the lattice of pclones on three-valued domain was reconstructed.
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