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Although the representations discussed here assume that each operator takes only a single object as input, it is possible to define a theoremproving representation that provides for multiple-input, single-output operators (Kowalski, 1972; see also Chap. ΧΠ, in Vol. m). Graph Representation In either a state-space or a problem-reduction representation, achieving the desired goal can be equated with finding an appropriate finite sequence of applications of available operators. While what one is primarily interested in—the goal situation or the sequence that leads to it—may depend on the problem, the term search can always be understood, without misleading consequences, as referring to the search for an appropriate operator sequence.
26 Search Π Tree structures are commonly used in implementing control strategies for the search. In a state-space representation, a tree may be used to represent the set of problem states produced by operator applications. In such a representation, the root node of the tree represents the initial problem situation or state. Each of the new states that can be produced from this initial state by the application of just one operator is represented by a successor node of the root node. Subsequent operator applications produce successors of these nodes, and so on.
In addition, combinations of forward and backward reasoning are possible. One important AI technique involving forward and backward reasoning is called means-ends analysis; it involves comparing the current goal with a current task-domain situation to extract a difference between them. This difference is then used to index the (forward) operator most relevant to reducing the difference. If this especially relevant operator cannot be immediately applied to the present problem state, subgoals are set up to change the problem state so that the relevant operator can be applied.
A Handbook of Active Filters by D.E. Johnson, etc.