On equational definability of function classes

Miguel Couceiro 1 Erkko Lehtonen 2 Tamas Waldhauser 3
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : We propose a notion of functional equation for functions of a fixed arity, which is based on a pair of clones. We present necessary conditions for aclass of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.
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Miguel Couceiro, Erkko Lehtonen, Tamas Waldhauser. On equational definability of function classes. Journal of Multiple-Valued Logic and Soft Computing, Old City Publishing, 2015, 24 (1–4), pp.203-222. ⟨hal-01093668⟩

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