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Машина Тьюринга:Распознавание четности - История изменений
2026-04-30T22:18:39Z
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WikiSysop: 1 версия
2008-08-04T09:55:52Z
<p>1 версия</p>
<p><b>Новая страница</b></p><div>Приведем пример [[машина Тьюринга|машины Тьюринга]], распознающую четные входные строки (пустую строку и строки состоящие из четного числа единиц).<br />
<br />
== Табличное представление МТ ==<br />
<latex><br />
\begin{tabular}{|cc|c|ccc|}<br />
\hline<br />
<br />
2bad & * & $\Rightarrow$ & [\textcolor{red}{q}] & 0 & \\ \hline<br />
2bad & 1 & $\Rightarrow$ & 2bad & * & L \\ \hline<br />
2ok & * & $\Rightarrow$ & [\textcolor{red}{q}] & 1 & \\ \hline<br />
2ok & 1 & $\Rightarrow$ & 2ok & * & L \\ \hline<br />
<\textcolor{blue}{even}> & * & $\Rightarrow$ & 2ok & * & L \\ \hline<br />
<\textcolor{blue}{even}> & 1 & $\Rightarrow$ & odd & 1 & R \\ \hline<br />
odd & * & $\Rightarrow$ & 2bad & * & L \\ \hline<br />
odd & 1 & $\Rightarrow$ & <\textcolor{blue}{even}> & 1 & R \\ \hline<br />
\end{tabular}<br />
</latex><br />
<code-python><br />
#<br />
# Распознавание четных строк (содержащих четное число "1").<br />
#<br />
MT={<br />
'k':1, <br />
'start': 'even',<br />
'stop': 'q',<br />
'program': {<br />
#(Состояние, символы на лентах) -> (новое состояние, (действия по каждой ленте))<br />
('even', ('*')): ('2ok', (('*','L'))), <br />
('even', ('1')): ('odd', (('1','R'))), <br />
('odd', ('1')): ('even', (('1','R'))), <br />
('odd', ('*')): ('2bad', (('*','L'))), <br />
('2ok', ('1')): ('2ok', (('*','L'))), <br />
('2ok', ('*')): ('q', (('1',''))), <br />
('2bad', ('1')): ('2bad', (('*','L'))), <br />
('2bad', ('*')): ('q', (('0',''))) <br />
}<br />
} <br />
</code-python><br />
<br />
== Графовое представление МТ ==<br />
<br />
<graph><br />
digraph G{rankdir=LR; edge[fontcolor="blue", fontsize="12", minlen="2", labeldistance="2", arrowhead="empty"]; <br />
<br />
"even"[shape="diamond"];<br />
"q"[shape="box"];"2bad"->"2bad" [headlabel="*L",taillabel="1"];<br />
"odd"->"2bad" [headlabel="*L",taillabel="*"];<br />
"odd"->"even" [headlabel="1R",taillabel="1"];<br />
"2bad"->"q" [headlabel="0",taillabel="*"];<br />
"2ok"->"q" [headlabel="1",taillabel="*"];<br />
"even"->"2ok" [headlabel="*L",taillabel="*"];<br />
"even"->"odd" [headlabel="1R",taillabel="1"];<br />
"2ok"->"2ok" [headlabel="*L",taillabel="1"];<br />
}<br />
</graph><br />
<br />
== Примеры выполнения МТ ==<br />
<br />
=== Пустая строка ===<br />
<pic-svg><br />
<svg<br />
xmlns:svg="http://www.w3.org/2000/svg"<br />
xmlns="http://www.w3.org/2000/svg"<br />
xmlns:xlink="http://www.w3.org/1999/xlink"<br />
version="1.0"<br />
width="140px"<br />
height="80px"<br />
><br />
<ellipse <br />
cx="50.0px"<br />
cy="30.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="100px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
</g> <br />
<ellipse <br />
cx="50.0px"<br />
cy="50.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
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<rect <br />
width="20px"<br />
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/><br />
</g> <br />
<ellipse <br />
cx="50.0px"<br />
cy="70.0px"<br />
rx="28px" <br />
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style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
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<rect <br />
width="20px"<br />
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x="100px"<br />
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</g> <br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="35px" ><br />
even</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="100px"<br />
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style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" ><br />
2ok</text><br />
<rect <br />
width="20px"<br />
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/><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
q</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="60px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="90.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
1</text><br />
</svg><br />
</pic-svg><br />
<br />
=== «111» ===<br />
<pic-svg><br />
<svg<br />
xmlns:svg="http://www.w3.org/2000/svg"<br />
xmlns="http://www.w3.org/2000/svg"<br />
xmlns:xlink="http://www.w3.org/1999/xlink"<br />
version="1.0"<br />
width="200px"<br />
height="200px"<br />
><br />
<ellipse <br />
cx="50.0px"<br />
cy="30.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="100px"<br />
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="120px"<br />
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width="20px"<br />
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1</text><br />
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<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" ><br />
1</text><br />
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" ><br />
1</text><br />
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
even</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="140px"<br />
y="60px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
1</text><br />
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
1</text><br />
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" ><br />
odd</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="160px"<br />
y="80px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" ><br />
1</text><br />
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" ><br />
1</text><br />
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" ><br />
2bad</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="140px"<br />
y="100px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" ><br />
1</text><br />
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" ><br />
1</text><br />
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" ><br />
2bad</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="120px"<br />
y="120px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" ><br />
1</text><br />
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="155px" ><br />
2bad</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="100px"<br />
y="140px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="155px" ><br />
1</text><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="175px" ><br />
2bad</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="160px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="195px" ><br />
q</text><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="180px"<br />
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"<br />
/><br />
<text x="90.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="195px" ><br />
0</text><br />
</svg><br />
</pic-svg><br />
<br />
=== «1111» ===<br />
<pic-svg><br />
<svg<br />
xmlns:svg="http://www.w3.org/2000/svg"<br />
xmlns="http://www.w3.org/2000/svg"<br />
xmlns:xlink="http://www.w3.org/1999/xlink"<br />
version="1.0"<br />
width="220px"<br />
height="240px"<br />
><br />
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cx="50.0px"<br />
cy="30.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
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width="20px"<br />
height="18.0px"<br />
x="80px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
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width="20px"<br />
height="18.0px"<br />
x="100px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="120px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
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width="20px"<br />
height="18.0px"<br />
x="140px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
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width="20px"<br />
height="18.0px"<br />
x="160px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
<rect <br />
width="20px"<br />
height="18.0px"<br />
x="180px"<br />
y="20px"<br />
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
</g> <br />
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cx="50.0px"<br />
cy="50.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
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width="20px"<br />
height="18.0px"<br />
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y="40px"<br />
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/><br />
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width="20px"<br />
height="18.0px"<br />
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y="40px"<br />
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width="20px"<br />
height="18.0px"<br />
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y="40px"<br />
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height="18.0px"<br />
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height="18.0px"<br />
x="180px"<br />
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"<br />
/><br />
</g> <br />
<ellipse <br />
cx="50.0px"<br />
cy="70.0px"<br />
rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
/><br />
<g> <br />
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height="18.0px"<br />
x="80px"<br />
y="60px"<br />
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/><br />
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ry="8px" <br />
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<g> <br />
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height="18.0px"<br />
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y="80px"<br />
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<g> <br />
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height="18.0px"<br />
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height="18.0px"<br />
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<rect <br />
width="20px"<br />
height="18.0px"<br />
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<rect <br />
width="20px"<br />
height="18.0px"<br />
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cx="50.0px"<br />
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rx="28px" <br />
ry="8px" <br />
style="fill:yellow;stroke:black;stroke-width:1"<br />
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<g> <br />
<rect <br />
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height="18.0px"<br />
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rx="28px" <br />
ry="8px" <br />
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<g> <br />
<rect <br />
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<rect <br />
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<rect <br />
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<rect <br />
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cx="50.0px"<br />
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rx="28px" <br />
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<g> <br />
<rect <br />
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<rect <br />
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<g> <br />
<rect <br />
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[[Category:Алгоритмы]]<br />
{{replicate-from-custiswiki-to-lib}}</div>
WikiSysop