since they do not lead to an improving state. However, the time spent in the detection of these actions may be not negligible.

The significance of the two techniques lies in that the overall time needed to solve the problems remains about the same, in the case where more irrelevant objects are used, and exactly the same, in the case where more resource levels are used. In the case of more irrelevant objects, these are detected (in negligible cost) and eliminated from the subsequent stages (Figure 6). However, there is some overhead imposed by the stages that precede the irrelevant objects elimination stage, from where these objects have not been eliminated.

In the case of more resource levels, these do not lead to the generation of new ground facts and actions, so all the pre-processing stages consume exactly the same time. As for the state-space search, this is also executed in the same time, but only in the case where neither the initial availability of resources, nor their consumption by the actions, nor finally the constraints over them have been changed. If this is not the case, then we are dealing with a different planning problem, which may be harder to solve.

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

## 8.4 Xor Constraints

We tested the efficiency of the XOR-constraints based decomposition in two domains: A simplified mystery domain, where resources have been removed, and the *grid* domain of the AIPS-98 competition. We did not use the *logistics* domain for these experiments, since *logistics* problems 