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@list l2 {mso-list-id:1061438774; mso-list-type:simple; mso-list-template-ids:-1069647046;}@list l2:level1 {mso-level-number-format:japanese-counting; mso-level-text:%1．; mso-level-tab-stop:21.0pt; mso-level-number-position:left; margin-left:21.0pt; text-indent:-21.0pt;}ol {margin-bottom:0cm;}ul {margin-bottom:0cm;}--></style><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="2050"/></xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--></head><body lang=ZH-CN style='tab-interval:21.25pt;text-justify-trim:punctuation' bgcolor="#e8ffe8"><div class=Section1><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanlang=EN-US style='font-size:18.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><span style="mso-spacerun: yes"> </span></span><spanstyle='font-size:18.0pt;mso-bidi-font-size:10.0pt;font-family:黑体;mso-ascii-font-family:"Times New Roman"'>按位异或及其在求解游戏策略问题中的应用</span><span lang=EN-US style='font-size:18.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanlang=EN-US style='font-size:18.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><b style='mso-bidi-font-weight:normal'><spanlang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><span style="mso-spacerun:yes"> </span></span></b><spanlang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><span style="mso-spacerun:yes"> </span><spanstyle="mso-spacerun: yes"> </span><spanstyle="mso-spacerun: yes"> </span></span><span style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:仿宋_GB2312;mso-ascii-font-family:"Times New Roman"'>李学武</span><spanlang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312'><o:p></o:p></span></p> <p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><spanstyle="mso-spacerun:yes"> </span></span><span style='font-size:9.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>（原载:《计算机科学》 2001.10）</span><spanlang=EN-US style='font-size:9.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><b style='mso-bidi-font-weight:normal'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>摘要</span></b><bstyle='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'> </span></b><span style='font-family:楷体_GB2312;mso-ascii-font-family:"Times New Roman"'>本文给出了关于按位异或运算的若干性质，在此基础上给出了该运算的两个较为重要的结果（定理</span><spanlang=EN-US style='mso-fareast-font-family:楷体_GB2312'>1</span><spanstyle='font-family:楷体_GB2312;mso-ascii-font-family:"Times New Roman"'>、定理</span><spanlang=EN-US style='mso-fareast-font-family:楷体_GB2312'>2</span><spanstyle='font-family:楷体_GB2312;mso-ascii-font-family:"Times New Roman"'>），并给出了它们在涉及到平衡态的游戏策略问题中的具体应用</span><spanlang=EN-US style='mso-fareast-font-family:楷体_GB2312'>. </span><spanstyle='font-family:楷体_GB2312;mso-ascii-font-family:"Times New Roman"'>有关结果未曾在其它资料中找到</span><spanlang=EN-US style='mso-fareast-font-family:楷体_GB2312'>.<o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><b style='mso-bidi-font-weight:normal'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>关键词</span></b><bstyle='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'> </span></b><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>异或；按位异或；游戏策略；</span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"'>平衡态<spanlang=EN-US><span style="mso-spacerun: yes"> </span></span></span><bstyle='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></b></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><b style='mso-bidi-font-weight:normal'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>中图分类号</span></b><bstyle='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></b></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>在下文中，</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>N<sup>*</sup></span><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>均表示非负十进制数的集合</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly;mso-layout-grid-align:none'><b style='mso-bidi-font-weight:normal'><spanlang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'>1 </span></b><b style='mso-bidi-font-weight:normal'><span style='font-size:14.0pt;mso-bidi-font-size:10.0pt;font-family:黑体;mso-ascii-font-family:"Times New Roman"'>按位异或的若干性质</span></b><bstyle='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:14.0pt;mso-bidi-font-size:10.0pt;mso-fareast-font-family:黑体'><o:p></o:p></span></b></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><spanstyle="mso-spacerun: yes"> </span></span><b style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>定义</span></b><bstyle='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>1</span></b><b style='mso-bidi-font-weight:normal'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>：（</span></b><bstyle='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>a</span></b><b style='mso-bidi-font-weight:normal'><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"'>⊙</span></b><b style='mso-bidi-font-weight:normal'><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>b</span></b><bstyle='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>）</span></b><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt'> </span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>设</span><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>a,b</span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"'>∈</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>{0,1}, </span><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>两个一位二进制数</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>a </span><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>b</span><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的异或</span><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>a</span><spanstyle='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"'>⊙</span><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>b</span><span style='font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的真值表如下：</span><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><o:p></o:p></span></p><p class=MsoNormal style='line-height:20.0pt;mso-line-height-rule:exactly'><spanlang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'><spanstyle="mso-spacerun: yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><o:p></o:p></span></p><table border=1 cellspacing=0 cellpadding=0 style='margin-left:89.4pt; border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt; mso-padding-alt:0cm 5.4pt 0cm 5.4pt'> <tr> <td width=98 valign=top style='width:73.5pt;border:solid windowtext .5pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='text-align:center;line-height:20.0pt; mso-line-height-rule:exactly'><span lang=EN-US style='font-size:12.0pt; mso-bidi-font-size:10.0pt'>a<o:p></o:p></span></p> </td> <td width=98 valign=top style='width:73.5pt;border:solid windowtext .5pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='text-align:center;line-height:20.0pt; mso-line-height-rule:exactly'><span lang=EN-US style='font-size:12.0pt; mso-bidi-font-size:10.0pt'>b <o:p></o:p></span></p> </td> <td width=98 valign=top style='width:73.5pt;border:solid windowtext .5pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='text-align:center;line-height:20.0pt; mso-line-height-rule:exactly'><span lang=EN-US style='font-size:12.0pt; mso-bidi-font-size:10.0pt'>a</span><span style='font-size:12.0pt;mso-bidi-font-size: 10.0pt;font-family:宋体;mso-hansi-font-family:"Times New Roman"'>⊙</span><span lang=EN-US style='font-size:12.0pt;mso-bidi-font-size:10.0pt'>b<o:p></o:p></span></p> </td> </tr> <tr> <td width=98 valign=top style='width:73.5pt;border:solid windowtext .5pt; border-top:none;mso-border-top-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='text-align:center;line-height:20.0pt; mso-line-height-rule:exactly'><span lang=EN-US style='font-size:12.0pt; mso-bidi-font-size:10.0pt'>1<o:p></o:p></span></p> </td> <td width=98 valign=top style='width:73.5pt;border-top:none;border-left:none; border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; padding:0cm 5.4pt 0cm 5.4pt'> <p class=MsoNormal align=center style='text-align:center;line-height:20.0pt; mso-line-height-rule:exactly'><span lang=EN-US style='font-size:12.0pt; mso-bidi-font-size:10.0pt'>1<o:p></o:p></span></p> </td> <td width=98 valign=top style='width:73.5pt;border-top:none;border-left:none; border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;⌨️ 快捷键说明
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