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Depending on the chip they use and your technical understanding of the chips inner workings. I would recommend to have a closer look at this paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.6043&rep=rep1&type=pdf
They developed a proof of concept software (debit) which helps to de-compile the bitstream, but only when the bit image is not encrypted (something I highly doubt in Avalons case, because those Xilinx chips with encryption features are quite expensive).
All the best!
one4many
P.S.: The paper is from 2008 ... so you might need to adjust the software (if you can it obtain it from somewhere).
LOL, that would something:) No idea if I can this one off though...
Thnx,
intron