Page 257 - Concise Encyclopedia of Robotics

PROBLEM REDUCTION
Complex problems can be made easier to solve by breaking them down
into small steps. This process is called problem reduction. It is an important
part of research in artificial intelligence (AI).
Two common forms
The proof of a mathematical theorem is a good exercise in problem reduc-
tion. Another way to develop this skill is to write computer programs in a
high-level language. Problem Reduction
When breaking a large, difficult problem down into small, easy steps,
one can lose sight of the overall picture. Keeping a mental image of the
goal, the progress being made, and the obstacles to come is a skill that
gets better and better with practice. You cannot sit down and prove pro-
found theorems in mathematics until you have learned to prove some
simple things first. The same holds true for smart computers and robots.
Theorem-proving machine
Suppose you build a theorem-proving machine (TPM) and assign it a
proposition, the proof of which is possible but difficult. Often, a mathe-
matician does not know, when setting out to prove something, if the
proposition is true. Thus, the mathematician does know if he or she can
solve the problem. In the example shown in the illustration, there are four

A
Desired
Start
result
B

C
D

Problem reduction

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