
$$\begin{array}{c c c}{{}}&{{}}&{{,}}\\ {{}}&{{}}&{{}}\\ {{\bf o p}G_{1}}&{{}}&{{\{P\},}}\\ {{}}&{{}}&{{\{P\},}}\\ {{}}&{{}}&{{\{P\},}}\\ {{}}&{{}}&{{\bf o p}P}\\ {{}}&{{}}&{{}}\\ {{\bf N}}&{{}}\\ {{\bf o p}G_{1}}&{{}}\end{array}\quad\begin{array}{c c c}{{}}&{{}}&{{,}}\\ {{}}&{{}}&{{}}\\ {{}}&{{}}&{{\bf o p}P}\\ {{}}&{{}}&{{}}\end{array}$$
 $\emptyset$  $\emptyset$  $\emptyset$  . 
$$\begin{array}{c}{{P}}\\ {{\{\ \mathbf{op}\,P\ \},\{\ \mathbf{op}G_{1}\ \ \mathbf{op}G_{2}\ \}\}}\end{array}$$

## 4.2  Solution Length Optimization

N
optimal

$$c a\,n$$

N

$$\mathbb{N}$$

![0_image_1.png](0_image_1.png)

![0_image_0.png](0_image_0.png)

$$2.1\;\;\;\;\mathrm{NO\,O\!I}$$

![0_image_2.png](0_image_2.png)

4.2.1 NOOPS-FIRST

![0_image_4.png](0_image_4.png)

![0_image_5.png](0_image_5.png)

.f

$$\mathrm{N}$$

![0_image_9.png](0_image_9.png)

i

 - $$\textbf{N}$$ $$\textbf{j}$$ $$\textbf{i}\ -$$ $$\textbf{N}$$ $$\textbf{f}$$. 

![0_image_6.png](0_image_6.png)

![0_image_8.png](0_image_8.png)

![0_image_10.png](0_image_10.png)

Proposition 3 Let  O',I,G  be a relaxed STRIPS task, which is solvable.  Using the NOOPs-first strategy, the plan that GRAPHPLAN returns will contain each action at most once.

Proof:
N
N
o

ooooooooooo ooo  N N o
N i .f

![0_image_3.png](0_image_3.png)

![0_image_7.png](0_image_7.png)

0 i,
.

f N
o f o o 20 t f.