Closed classes of functions, generalized constraints and clusters

Abstract:  Classes of functions of several variables on arbitrary nonempty domains that are closed under permutation of variables and addition of dummy variables are characterized by generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary nonempty domains that are closed under permutation of variables, addition of dummy variables, and composition are characterized by clusters, and a Galois connection is established between operations and clusters.

Keyword(s):  function algebra ; closed set ; generalized constraint ; cluster ; Galois connection

Publication Year:   2010

Research Unit:   University of Luxembourg, FSTC, CSC

Reference:  Algebra Universalis, 63 (2010), no. 2-3, pp. 203-234

Full text available on :   http://dx.doi.org/10.1007/s00012-010-0071-6 (This access could be restricted and is not under UL responsibility)