Dog feces will decompose naturally but not fast enough to keep your yard clean if you have a dog. This site explains how to make a composter for dog feces. Basically it's like an 'out house' for the dog, except you have to collect & deposit. I know someone who tried it and it took an amazing long time until it needed to be filled with dirt, sodded over & moved.
http://www.plantea.com/dog-waste-compost.htm