New Conditions for Taylor Varieties and CSP

We provide two new characterizations for finitely generated varieties with Taylor terms. The first characterization is using "absorbing sets" and the second one "cyclic operations". These new conditions allow us to reprove the conjecture of Bang-Jensen and Hell (proved by the authors, comp. STOC\´08, SICOMP\´09) and the characterization of locally finite Taylor varieties using weak near-unanimity operations (proved by McKenzie and Maroti, Alg.Univ. 2009) in an elementary and self-contained way. The research is closely connected to the algebraic approach to CSP and previous results obtained by authors using similar tools [comp. STOC\´08, SICOMP\´09, FOCS\´09 etc.].