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### Heuristic Functions

**
Definition
**
**
– Solution Distance
**

Let
*
(S, s
_{
0
}
*

*,*

*succ*

*, Sol)*

*be a search scheme. The solution distance*

*sd(s*

*)*of a state s ∈ S is the length of a shortest

*succ*path from

*s*to a state in

*Sol*, or 1 if there is no such path. Computing the real solution distance is as hard as solving the problem itself.

**Speaker notes:**