By minimal K-T resolution you mean a CDGA which as an algebra $\mathcal A$ is a polynomial algebra on a nonnegatively graded vector space and whose differential lands in $\mathcal A^+\cdot\mathcal A^+$ q-iso to your initial algebra $A$?
– Mariano Suárez-Alvarez♦Jul 23 '13 at 6:32