Backdoors measure the distance to tractable fragments and have become an important tool to find fixed-parameter tractable (fpt) algorithms. Despite their success, backdoors have not been used for planning, a central problem in AI that has a high computational complexity. In this work, we introduce two notions of backdoors building upon the causal graph. We analyze the complexity of finding a small backdoor (detection) and using the backdoor to solve the problem (evaluation) in the light of planning with (un)bounded plan length/domain of the variables. For each setting we present either an fpt-result or rule out the existence thereof by showing parameterized intractability. In three cases we achieve the most desirable outcome: detection and evaluation are fpt.

What determines difficulty of solving a problem? Although this question has been studied before, we found examples which show large differences in problem difficulty which are not explained by concepts identified in previous research. This differences are caused mainly by the structure of a problems' state spaces and cannot be easily captured by static metrics like size of the state space or the length of a solution. To address these unexplained differences, we propose a computational model of human problem solving behaviour. We provide evaluation of the model over large scale dataset (hundreds of hours of problem solving, more than 100 problem instances) for three transport puzzles (Sokoban, Rush hour, and Replacement puzzle).