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The max-Lukasiewicz semiring is defined as the unit interval [0, 1] equipped with the arithmetics “a+ b”= max (a, b) and “ab”= max (0, a+ b− 1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-Lukasiewicz semiring.