Variable resolution Associative Memory use and optimization for the Fast Tracker ATLAS upgrade

The most recent prototype of the Associative Memory (AM) chip developed for the ATLAS Fast Tracker includes ternary logic cells that can store 0, 1, or "don't care" values. This allows an enormous flexibility, with the possibility to program the precision of the spatial coincidence for each pattern and for each detector layer. We call this use of the associative memory: "variable resolution pattern recognition". A technique that can be applied to any coincidence based trigger. We describe an advanced technique to build the bank of patterns for the associative memory. Full resolution patterns are merged and split (profiting of variable resolution) to obtain the optimal set of patterns that fits in a given AM size while providing the best rejection of random coincidences without loss in efficiency