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<div style='text-align:right;position:absolute;top:92.0%;left:72.65%;
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<div style='position:absolute;top:3.75%;left:5.05%;width:93.07%;height:5.25%'><span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>5.<span
style="mso-spacerun: yes"> </span></span><span lang=ZH-CN
style='mso-fareast-language:ZH-CN'>若</span><span lang=ZH-CN style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman";mso-fareast-language:
ZH-CN'> </span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>W1, W2</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'> </span><span lang=ZH-CN style='mso-fareast-language:
ZH-CN'>是公式</span><span lang=ZH-CN style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'>, </span><span
lang=ZH-CN style='mso-fareast-language:ZH-CN'>则 </span></div>
<div style='position:absolute;top:8.75%;left:5.05%;width:93.07%;height:5.75%'><span
lang=ZH-CN style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><span style="mso-spacerun:
yes"> </span></span><span lang=EN-US style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman";mso-fareast-language:
ZH-CN'><i>R[W1</i></span><span lang=EN-US style='font-family:Symbol;
mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>Ù</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>W2]=R[W1]</i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>Ù</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R[W2], </i></span></div>
<div style='position:absolute;top:14.0%;left:5.05%;width:93.07%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i><span style="mso-spacerun:
yes"> </span>R[W1</i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>Ú</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>W2]=R[W1]</i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>Ú</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R[W2], </i></span></div>
<div style='position:absolute;top:19.5%;left:5.05%;width:93.07%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i><span style="mso-spacerun:
yes"> </span>R[W1</i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>®</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>W2]=R[W1] </i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>®</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> R[W2]</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:25.5%;left:5.05%;width:93.07%;height:4.75%'><span
lang=EN-US style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:30.5%;left:5.05%;width:93.07%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R </i></span>减少<span style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman"'> </span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>do </i></span>的数目<span style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman"'>, </span>即嵌套的状态<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>. </span></div>
<div style='position:absolute;top:35.75%;left:5.05%;width:93.07%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R[G] </i></span><span lang=ZH-CN
style='mso-fareast-language:ZH-CN'>把目标回归为从</span><span lang=ZH-CN
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'> </span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>S0 </i></span><span
lang=ZH-CN style='mso-fareast-language:ZH-CN'>执行动作序列的结果</span><span
lang=ZH-CN style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'>. </span></div>
<div style='position:absolute;top:41.0%;left:5.05%;width:93.07%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R_0[G]=G, </i></span></div>
<div style='position:absolute;top:46.5%;left:5.05%;width:93.07%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>R_n[G]=R[R_(n-1)[G]],<span style="mso-spacerun:
yes"> </span>n=1,2,… </i></span></div>
<div style='position:absolute;top:52.25%;left:5.05%;width:93.07%;height:4.75%'><span
lang=EN-US style='mso-fareast-language:ZH-CN;display:none'><i> </i></span></div>
<div style='position:absolute;top:57.5%;left:5.05%;width:93.07%;height:4.75%'><span
lang=EN-US style='font-family:黑体;mso-ascii-font-family:黑体;mso-fareast-font-family:
黑体;mso-fareast-language:ZH-CN'>10.5.4<span style="mso-spacerun: yes">
</span></span><span lang=ZH-CN style='font-family:黑体;mso-ascii-font-family:
黑体;mso-fareast-font-family:黑体;mso-fareast-language:ZH-CN'>规划方法</span><i> </i></div>
<div style='position:absolute;top:62.0%;left:5.05%;width:93.07%;height:5.75%'><span
style='font-family:黑体;mso-fareast-font-family:黑体'>定理</span><span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'><span
style="mso-spacerun: yes"> </span></span>一个行动序列<span style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman"'><i> a</i></span>对于<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>
</span><span style='font-family:Symbol;mso-char-type:symbol'>S</span><span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>
</span>是合法的<span style='font-family:"Times New Roman";mso-ascii-font-family:
"Times New Roman"'>, iff </span></div>
<div style='position:absolute;top:67.25%;left:5.05%;width:111.79%;height:5.75%'><span
lang=EN-US style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:
symbol'><i>S</i></span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>_(unt) </i></span><span
lang=EN-US style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:
symbol'><i>ÈS</i></span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>_(S0)
|= </i></span><span lang=EN-US style='font-family:Symbol;mso-fareast-language:
ZH-CN;mso-char-type:symbol'><i>Ù</i></span><span lang=EN-US style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman";mso-fareast-language:
ZH-CN'><i>_i R_(i-1)[(precond(ai,do([a1,…,a_(I-1),S0))]</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><span style="mso-spacerun: yes">
</span> </span></div>
<div style='position:absolute;top:73.5%;left:5.05%;width:93.07%;height:4.75%'><span
lang=EN-US style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:78.0%;left:5.05%;width:93.07%;height:5.75%'><span
style='font-family:黑体;mso-fareast-font-family:黑体'>定理</span><span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'><span
style="mso-spacerun: yes"> </span></span><span lang=EN-US
style='font-family:Symbol;mso-ansi-language:EN-US;mso-char-type:symbol'><i>S</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-ansi-language:EN-US'><i> |= </i></span><span lang=EN-US style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman";mso-fareast-language:
ZH-CN'><i>Q(do([a1,…,an]),S0))<span style="mso-spacerun: yes">
</span>iff </i></span></div>
<div style='position:absolute;top:83.25%;left:5.05%;width:95.5%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i><span style="mso-spacerun:
yes">
</span></i></span><span lang=EN-US style='font-family:Symbol;mso-fareast-language:
ZH-CN;mso-char-type:symbol'><i>S</i></span><span lang=EN-US style='font-family:
"Times New Roman";mso-ascii-font-family:"Times New Roman";mso-fareast-language:
ZH-CN'><i>_(unt) </i></span><span lang=EN-US style='font-family:Symbol;
mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>È</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'> </span><span lang=EN-US style='font-family:Symbol;
mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>S</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>_(S0) |=</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'> </span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>R_n[Q(do[a1,…,an],S0))].</i></span><span
lang=EN-US style='mso-fareast-language:ZH-CN;mso-special-format:lastCR;
display:none'> </span></div>
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