1. Problem Characteristics
Is the problem decomposable?
Can solution steps be ignored or undone?
Is the universe predictable?
Is a good solution absolute or relative?
Is the solution a state or a path?
What is the role of knowledge?
Does the task require interaction with a person?

2. Production system characteristics
Monotonic: execution of a rule never prevents the execution of other applicable rules
Non-monotonic: without this property
Partially commutative: if application of a particular sequence of rules transforms state x into state y, then any permutation of those rules that are allowable, transforms x into y
Commutative: monotonic + partially commutative

3. Problems and production system
monotonic
Non-monotonic
Partially commutative
Theorem proving
Robot navigation
Non-partially commutative
Chemical synthesis
backgammon

4. Problems and production system
monotonic
Non-monotonic
Partially commutative
Ignorable
Recoverable
Non-partially commutative
Irrecoverable
Unpredictable

5. Sample problems - 8-puzzle

6. Sample problems - 8-puzzle

7. Sample problems - 8 queens

8. Sample problems - 8 queens

9. Sample problems - 8 queens

10. Sample problems - Cryptarithmetic

11. Sample problems - Cryptarithmetic