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PDDL2.1, that was used for IPC3 introduces the notion of durative actions**. A durative**
action represents an interval of time, and conditions and effects can be associated with either endpoint of this interval. Durative actions can also **have invariant conditions that**
must hold for the entire duration of the action.

We use the constraint-based interval **approach to temporal POCL planning described by**
Smith et al. (2000), which in essence is the same approach as used by earlier temporal POCL
planners such as DEVISER **(Vere, 1983),** ZENO **(Penberthy & Weld, 1994), and** IxTeT
(Ghallab & Laruelle, 1994). Like IxTeT**, we use a simple temporal network (STN) to record**
temporal constraints. The STN representation allows for rapid response to temporal queries.

ZENO, on the other hand, uses an integrated approach for handling **both temporal and**
metric constraints, and does not make use of techniques optimized for temporal reasoning.

The following is a description of how VHPOP **handles the type of temporal planning**
domains expressible in PDDL2.1.

When planning with durative actions, we substitute the partial order O in the representation of a plan with an STN T . Each action ai **of a plan, except the dummy actions**
a0 and a∞, is represented by two nodes t2i−1 (start time) and t2i **(end time) in the STN**
T , and T can be compactly represented by the d-graph **(Dechter et al., 1991). The d-graph**
is a complete directed graph, where each edge ti → tj **is labeled by the shortest temporal**
distance, dij , between the two time nodes ti and tj (i.e. tj − ti ≤ dij **). An additional time**