Many cognitive models might approach this by assuming the crow has a big table of "knowledge" that it can logically manipulate to deduce an answer: "stick can reach food from entrance to log," "I can get stick if I go over there," "I can move stick to entrance of log," => "I can reach food." This paper, however, proposes a much more general and simple model: the crow lives by the rule "I'll do whatever will maximize the number of different world states my world can be in 5 seconds from now." By this principle, the crow can reach a lot more states if it can move the stick (instead of the fewer states where the stick just sits in the same place on the ground), so it heads over towards the stick. Now it can reach a lot more states if it pokes the food out of the hole with the stick, so it does. And now, it can eat the tasty food.
But the cow could reach even more states if it broke the stick into thousand little pieces and scattered them all over the place. No tasty food here.