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Additional info for Admissible heuristics for automated planning
G. by Chapman (1987), Bylander (1991) and others) the problem model was simplified and the background theories discarded. g. Wilkins, 1983). 2 of PDDL (Edelkamp & Hoffmann 2004). 2 allows so called derived predicates, which are defined by a set of rules evaluated recursively (in PROLOG style), rather than part of the world state. , the transitive closure of a relation to be expressed, but is still compilable into the basic representation (Thiebaux, Hoffmann, & Nebel 2003). The state variable representation (B¨ ackstr¨ om 1992; Sandewall & R¨onnquist 1986) replaces the logical propositions of the STRIPS representation by variables with finite ranges of values, but embodies the same planning model: in fact, it is expressively equivalent with propositional STRIPS (for each variable v and value c, “v = c” is essentially a proposition; a formal proof of equivalence is given by B¨ackstr¨om, 1992).
However, when an atom set s is stored in the table, every set that is a prefix of s (viewed as a string with atoms in lexical order) must also be stored, with value 0 if no better value is available. With most methods of computing heuristic values this does not present a problem since whenever a set is stored, all its subsets (including subsets corresponding to lexical prefixes) have already been stored. Even so, there is some overhead compared to a table and evaluation procedure designed for a fixed maximal subset size.
On-Table A) (on B A) (on B A) ... noop (on-Table B) noop (clear A) noop (on-Table A) (move-from-table A B) (on A B) (move-to-table B A) (clear A) (move-from-table A C) (on A C) (move B A C) (on B C) ... noop (clear B) ... (move-from-table C B) (on C B) ... (clear B) (clear C) noop (move C B A) (clear C) (move-from-table C A) (on-Table C) noop (on C A) ... (on-Table C) (move-from-table C B) (on C B) ... 1. Only a few mutex relations are shown (the dashed arrows connecting atoms/actions in the same layer).