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<P class=MsoNormal style="TEXT-ALIGN: center" align=center><B style="mso-bidi-font-weight: normal"><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" preferrelative="t" spt="75" coordsize="21600,21600"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 9pt; HEIGHT: 3.75pt" type="#_x0000_t75" ole=""><v:imagedata title="" src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape></B><B style="mso-bidi-font-weight: normal">第二章</B><B style="mso-bidi-font-weight: normal"><p></p></B></P>
<P class=MsoNormal>6、令文法G<SUB>6</SUB>为：N → D|ND</P>
<P class=MsoNormal> D → 0|1|2|3|4|5|6|7|8|9<p></p></P>
<P class=MsoNormal> （1）G<SUB>6 </SUB>的语言L（G<SUB>6</SUB>）是什么？<p></p></P>
<P class=MsoNormal> （2）给出句子0127、34和568的最左推导和最右推导。<p></p></P>
<P class=MsoNormal>解答：<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">思路：由N → D|ND可得出如下推导N＝＞ND＝＞NDD＝＞…＝＞D<SUP>n</SUP>（n＞=1） 可以看出，N最终可以推导出1个或多个（也可以是无穷）D，而D → 0|1|2|3|4|5|6|7|8|9可知，每个D为0～9中的任一个数字，所以，N 最终推导出的就是由0～9这10个数字组成的字符串。<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5">（1）G<SUB>6 </SUB>的语言L（G<SUB>6</SUB>）是由0～9这10个数字组成的字符串,或{0，1,…,9}<SUP>+</SUP>。<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">(2)句子0127、34和568的最左推导分别为:<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞NDD＝＞NDDD＝＞DDDD＝＞0DDD＝＞01DD＝＞012D＝＞0127<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞DD＝＞3D＝＞34<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞NDD＝＞DDD＝＞5DD＝＞56D＝＞568<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">句子0127、34和568的最右推导分别为:<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞N7＝＞ND7＝＞N27＝＞ND27＝＞N127＝＞D127＝＞0127<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞N4＝＞D4＝＞34<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 21pt">N＝＞ND＝＞N8＝＞ND8＝＞N68＝＞D68＝＞568<p></p></P>
<P class=MsoNormal>7、写一个文法，使其语言是奇数集，且每个基数不以0开头。<p></p></P>
<P class=MsoNormal>解答：G（S）：S → CD|D D→1|3|5|7|9<p></p></P>
<P class=MsoNormal> C → CB|A A→2|4|6|8|D<p></p></P>
<P class=MsoNormal> B → A|0<p></p></P>
<P class=MsoNormal> 或：<p></p></P>
<P class=MsoNormal> G（S）：S →MWN|N N →1|3|5|7|9 M →1|2|3|4|5|6|7|8|9<p></p></P>
<P class=MsoNormal> W → WV|ε V → M|0<p></p></P>
<P class=MsoNormal>8、令文法为 ：<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 42pt; mso-char-indent-count: 4.0"> E→T|E+T|E-T<p></p></P>
<P class=MsoNormal> T→F|T*F|T/F<p></p></P>
<P class=MsoNormal> F→（E）|i<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 5.25pt; mso-char-indent-count: .5; mso-para-margin-left: 1.0gd">（1）i+i*i、i*（i+i）的最左推导和最右推导；<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 5.25pt; mso-char-indent-count: .5; mso-para-margin-left: 1.0gd">（2）给出i+i+i、i+i*i和i-i-i的语法树。<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 5.25pt; mso-char-indent-count: .5; mso-para-margin-left: 1.0gd">解答：<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 5.25pt; mso-char-indent-count: .5; mso-para-margin-left: 1.0gd">（1）i+i*i、i*（i+i）的最左推导分别为：<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">E＝＞T＝＞E+T＝＞F+T＝＞i+T＝＞i+T*F＝＞i+F*F＝＞i+i*F＝＞i+i*i<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">E＝＞T＝＞T*F＝＞F*F＝＞i*F＝＞i*（E）＝＞i*（E+T）＝＞i*（T+T）＝＞i*（F+T）<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">＝＞i*（i+T）＝＞i*（i+F）＝＞i*（i+i）<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">i+i*i、i*（i+i）的最右推导分别为：<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">E＝＞T＝＞E+T＝＞E+T*F＝＞E+T*i＝＞E+F*i＝＞E+i*i＝＞T+i*i<p></p></P>
<P class=MsoNormal style="MARGIN-LEFT: 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd">＝＞F+i*i＝＞i+i*i<p></p></P>
<P class=MsoNormal style="MARGIN: 12pt 0cm 0pt 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd; mso-para-margin-top: 12.0pt; mso-para-margin-right: 0cm; mso-para-margin-bottom: .0001pt">E＝＞T＝＞T*F＝＞T*（E+T）＝＞T*（E+F）＝＞T*（E+i）＝＞T*（T+i）<p></p></P>
<P class=MsoNormal style="MARGIN: 12pt 0cm 0pt 10.5pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-para-margin-left: 1.0gd; mso-para-margin-top: 12.0pt; mso-para-margin-right: 0cm; mso-para-margin-bottom: .0001pt">＝＞T*（F+i）＝＞T*（i+i）＝＞F*（i+i）＝＞i*（i+i）<p></p></P>
<P class=MsoNormal style="TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5"><v:group id=_x0000_s1054 style="MARGIN-TOP: 19.5pt; Z-INDEX: 17; LEFT: 0px; MARGIN-LEFT: 328pt; WIDTH: 56pt; POSITION: absolute; HEIGHT: 27pt; TEXT-ALIGN: left" coordsize="1120,434" coordorigin="4197,2746"><v:line id=_x0000_s1055 style="POSITION: absolute" to="4838,3180" from="4837,2746"></v:line><v:line id=_x0000_s1056 style="POSITION: absolute; flip: x" to="4677,3180" from="4197,2746"></v:line><v:line id=_x0000_s1057 style="POSITION: absolute" to="5317,3180" from="4998,2746"></v:line></v:group><v:group id=_x0000_s1026 style="MARGIN-TOP: 19.5pt; Z-INDEX: 1; LEFT: 0px; MARGIN-LEFT: 184pt; WIDTH: 56pt; POSITION: absolute; HEIGHT: 27pt; TEXT-ALIGN: left" coordsize="1120,434" coordorigin="4197,2746"><v:line id=_x0000_s1027 style="POSITION: absolute" to="4838,3180" from="4837,2746"></v:line><v:line id=_x0000_s1028 style="POSITION: absolute; flip: x" to="4677,3180" from="4197,2746"></v:line><v:line id=_x0000_s1029 style="POSITION: absolute" to="5317,3180" from="4998,2746"></v:line></v:group>（2） E E E</P>
<P class=MsoNormal><v:group id=_x0000_s1040 style="MARGIN-TOP: 0px; Z-INDEX: 9; LEFT: 0px; MARGIN-LEFT: 1in; WIDTH: 56pt; POSITION: absolute; HEIGHT: 27pt; TEXT-ALIGN: left" coordsize="1120,434" coordorigin="4197,2746"><v:line id=_x0000_s1041 style="POSITION: absolute" to="4838,3180" from="4837,2746"></v:line><v:line id=_x0000_s1042 style="POSITION: absolute; flip: x" to="4677,3180" from="4197,2746"></v:line><v:line id=_x0000_s1043 style="POSITION: absolute" to="5317,3180" from="4998,2746"></v:line></v:group> </P>
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<P class=MsoNormal><v:line id=_x0000_s1044 style="Z-INDEX: 10; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left" to="1in,21.7pt" from="1in,0"></v:line><p> </p></P><br style="mso-ignore: vglayout" clear=all>
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<P class=MsoNormal><v:line id=_x0000_s1045 style="Z-INDEX: 11; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left" to="1in,21.7pt" from="1in,0"></v:line><p> </p></P><br style="mso-ignore: vglayout" clear=all>
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<P class=MsoNormal style="TEXT-INDENT: 15.75pt; mso-char-indent-count: 1.5"> i+i+I i+i*i</P>
<P class=MsoNormal> i i-i-i </P>
<P class=MsoNormal style="MARGIN-TOP: 12pt">9、证明下面的文法是二义的： S→iSeS|iS|i<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 9pt; mso-line-height-rule: exactly">证明：<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> 思路：要证明该文法是二义的，必须找到一个句子，使得该句子具有两个不同的最右<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly">推导或两个不同的语法树。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> 对于句子iiiei，存在如下两个最右推导：<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> S＝＞iSeS＝＞iSei＝＞iiSei＝＞iiiei<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> S＝＞iS＝＞iiSeS＝＞iiSei＝＞iiiei<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> 由此，该文法是二义的。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly">10、把下面文法改写为无二义的：S→SS|（S）|（）<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly">解答：思路：对于句子（）（）（），存在如下两棵语法树，所以该文法是二义性文法，引起<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> S S<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"><v:group id=_x0000_s1072 style="MARGIN-TOP: 8.25pt; Z-INDEX: 27; LEFT: 0px; MARGIN-LEFT: 64pt; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1073 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1074 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group><v:group id=_x0000_s1084 style="MARGIN-TOP: 4.5pt; Z-INDEX: 31; LEFT: 0px; MARGIN-LEFT: 267pt; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1085 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1086 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group><p> </p></P><br style="mso-ignore: vglayout" clear=all>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> S S S S<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"><v:group id=_x0000_s1093 style="MARGIN-TOP: 5.75pt; Z-INDEX: 34; LEFT: 0px; MARGIN-LEFT: 91.5pt; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1094 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1095 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group><v:group id=_x0000_s1090 style="MARGIN-TOP: 1.25pt; Z-INDEX: 33; LEFT: 0px; MARGIN-LEFT: 244.5pt; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1091 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1092 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group><v:group id=_x0000_s1087 style="MARGIN-TOP: 0.5pt; Z-INDEX: 32; LEFT: 0px; MARGIN-LEFT: 4in; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1088 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1089 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group><v:group id=_x0000_s1069 style="MARGIN-TOP: 5.75pt; Z-INDEX: 26; LEFT: 0px; MARGIN-LEFT: 40pt; WIDTH: 40pt; POSITION: absolute; HEIGHT: 22.5pt; TEXT-ALIGN: left" coordsize="800,450" coordorigin="2917,2655"><v:line id=_x0000_s1070 style="POSITION: absolute; flip: x" to="3237,3105" from="2917,2670"></v:line><v:line id=_x0000_s1071 style="POSITION: absolute" to="3717,3090" from="3397,2655"></v:line></v:group> <p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> S S （ ） （ ）S S<p></p></P>
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<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 5.25pt; LINE-HEIGHT: 11pt; mso-char-indent-count: .5; mso-line-height-rule: exactly">（ ）（ ） （ ）（ ）<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> 二义性的原因在于S→SS，可将其改造成等价的递归结构，消除二义性。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> 改造后的文法为：S→TS|T T→（S）|（）<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly">11、给出下面语言的相应文法： L1={a<SUP>n</SUP>b<SUP>n</SUP>c<SUP>i</SUP>|n>=1,i>=0}<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> L2={a<SUP>i</SUP>b<SUP>n</SUP>c<SUP>n</SUP>|n>=1,i>=0}<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> L3={a<SUP>n</SUP>b<SUP>n</SUP>a<SUP>m</SUP>b<SUP>m</SUP>|n,m>=0}<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 11pt; mso-line-height-rule: exactly"> L4={1<SUP>n</SUP>0<SUP>m</SUP>1<SUP>m</SUP>0<SUP>n</SUP>|n,m>=0}<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 18pt; mso-line-height-rule: exactly; tab-stops: 49.5pt">解答: <p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-char-indent-count: 2.0; mso-line-height-rule: exactly; tab-stops: 49.5pt">分析:L1:要求a和b的个数一样多,并至少为1个,c的个数为0个以上,可用一个非终结符去生成a<SUP>n</SUP>b<SUP>n </SUP>串,一个非终结符生成c<SUP>i</SUP>;L2同L1。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-char-indent-count: 2.0; mso-line-height-rule: exactly; tab-stops: 49.5pt">L3:将a<SUP>n</SUP>b<SUP>n</SUP>a<SUP>m</SUP>b<SUP>m</SUP>分为两段考虑, a<SUP>n</SUP>b<SUP>n</SUP>和a<SUP>m</SUP>b<SUP>m</SUP>,然后使用两个终结符分别产生。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-char-indent-count: 2.0; mso-line-height-rule: exactly; tab-stops: 49.5pt">L4:采用从里往外扩展的方式,先用一个非终结符生成中间的m个0和m个1,然后，再用另一个非终结符在该串的基础上扩充前后的n个0和n个1。<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; LINE-HEIGHT: 18pt; mso-line-height-rule: exactly; tab-stops: 49.5pt"> L1的文法: S→AC A→aAb|ab C→Cc|ε<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-line-height-rule: exactly; tab-stops: 49.5pt">L2的文法: S→AB A→Aa|ε B→bBc|bc<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-line-height-rule: exactly; tab-stops: 49.5pt">L3的文法: S→AB A→aAb|ε B→aBb|ε<p></p></P>
<P class=MsoNormal style="MARGIN-TOP: 12pt; TEXT-INDENT: 21pt; LINE-HEIGHT: 18pt; mso-line-height-rule: exactly; tab-stops: 49.5pt">L4的文法: S→1A0|A A→0A1|ε<p></p></P></div><div id="Message" class="Message"></div><br>
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