Suppose that we are using PDDL to describe facts and actions in a certain world called JUNGLE. In the JUNGLE world there are 4 predicates, each predicate takes at most 4 arguments, and there are 5 constants. Give a reasonably tight bound on the number of unique states in the JUNGLE world. Justify your answer.

PDDL (the "Planning Domain Definition Language") is a recent attempt to standardise planning domain and problem description languages. It was developed mainly to make the International Planning Competition (IPC) series possible. The planning competition compares the performance of planning systems on sets of benchmark problems, so a common language for specifying problems must be used.

PDDL contains STRIPS, ADL and much, much more. Most planners, however, do not support full PDDL. The majority support only the STRIPS subset, or some small extension of it. PDDL has evolved over time, with minor and major revisions published at each planning competition: generally recognised versions are 1.0 (used in IPC 1998), 2.0 (used in IPC 2000), 2.1 (used in IPC 2002), 2.2 (used in IPC 2004), 3.0 (used in IPC 2006) and 3.1 (used in IPC 2008).

Important note: As mentioned above, most planners do not support all elements of (any version of) PDDL. Moreover, many planners have their own little "excentricities", meaning that they may interpret certain PDDL constructs incorrectly, or require minor variations in syntax that is at odds with the official language specification. Some examples:

Some planners have an implicit constraint that all arguments to an action are distinct.

Some planners require action preconditions and/or effects to be written as conjunctions (i.e., as (and ...)) even when the precondition/effect contains only one atomic condition, or even no condition at all.

Explanation:

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