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Platform. All the experiments were run on a Pentium III Xeon 700MHz with 6GB RAM running Linux. For each run, we fix a memory limit of 512MB and a CPU time limit of 1 hour. For each problem instance, we report both the CPU time (in seconds) required to find a solution for the given planning problem, and the length of the generated plan. For CFF and KACMBP we report total times. In the case of KACMBP this includes constructing the BDD-based representation of the automaton, and the computation of the heuristic information.

For KACMBP, the encodings are written in SMV language. Similar to CPLAN and DLVk , we use scalar variables, that are logarithmically encoded in booleans. We remark that the static analysis tools like Stan [31] and Discoplan [32] would be able (at least in deterministic domains) to detect and eliminate constant predicates, and partition atoms into groups of mutually exclusive facts. CFF uses propositional encodings written in a variation of PDDL. DLVk is able to express parallel encodings, and to express incomplete knowledge by an appropriate “knowledge-based” modeling.

The intuition is that if a knowledge formulae φ is necessary, basically there is no way to solve the problem without coming to know φ at some point, in the sequence of belief states traversed during the execution of any solution plan. In the case of the problem depicted in Fig. 22 it is clear that it is impossible to reach the goal without coming to know the value of y: this means that there is no sequence of belief states associated with a solution plan that does not “enter” the denotation of Ky.

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