Просмотр исходного текста страницы Машина Тьюринга:Унарное сложение

Приведем пример [[машина Тьюринга|машины Тьюринга]], выполняющей унарное сложение двух операндов.
Операнды представляются в унарной системе, т. к. целое неотрицательное число ''n'' представляется ''n+1'' единицей.

== Табличное представление МТ ==
<latex>
\begin{tabular}{|cc|c|ccc|}
\hline
    
 <\textcolor{blue}{1pass}> & * & $\Rightarrow$ & 2pass & 1 & R \\ \hline
 <\textcolor{blue}{1pass}> & 1 & $\Rightarrow$ & <\textcolor{blue}{1pass}> & 1 & R \\ \hline
 2pass & * & $\Rightarrow$ & del1 & * & L \\ \hline
 2pass & 1 & $\Rightarrow$ & 2pass & 1 & R \\ \hline
 del1 & 1 & $\Rightarrow$ & del2 & * & L \\ \hline
 del2 & 1 & $\Rightarrow$ & rewind & * & L \\ \hline
 rewind & * & $\Rightarrow$ & [\textcolor{red}{q}] & * & R \\ \hline
 rewind & 1 & $\Rightarrow$ & rewind & 1 & L \\ \hline
\end{tabular}
</latex>
<code-python>
MT={
 'k':1, 
 'start': '1pass',
 'stop': 'q',
 'program': {
 #(Состояние, символы на лентах) -> (новое состояние, (действия по каждой ленте))
  ('1pass', ('1')):         ('1pass', (('1','R'))), # проходим первое число
  ('1pass', ('*')):         ('2pass', (('1','R'))), # меняем разделитель
  ('2pass', ('1')):         ('2pass', (('1','R'))), # проходим второе число 
  ('2pass', ('*')):         ('del1',  (('*','L'))), # конец второго числа 
  ('del1',  ('1')):         ('del2',  (('*','L'))), # удаляем первую лишнюю 1
  ('del2',  ('1')):         ('rewind',(('*','L'))), # удаляем вторую лишнюю 1
  ('rewind',('1')):         ('rewind',(('1','L'))), # перематываем к началу. 
  ('rewind',('*')):         ('q',     (('*','R')))  # конец.
 }
}  
</code-python>

== Графовое представление МТ ==

<graph>
 digraph G{rankdir=LR; edge[fontcolor="blue", fontsize="10", minlen="2", labeldistance="2",  arrowhead="empty"]; 

 "1pass"[shape="diamond"];
 "q"[shape="box"];"del1"->"del2" [headlabel="*L",taillabel="1"];
 "1pass"->"1pass" [headlabel="1R",taillabel="1"];
 "del2"->"rewind" [headlabel="*L",taillabel="1"];
 "1pass"->"2pass" [headlabel="1R",taillabel="*"];
 "2pass"->"del1" [headlabel="*L",taillabel="*"];
 "rewind"->"q" [headlabel="*R",taillabel="*"];
 "rewind"->"rewind" [headlabel="1L",taillabel="1"];
 "2pass"->"2pass" [headlabel="1R",taillabel="1"];
}
</graph>

== Примеры выполнения МТ ==

=== «1» + «1» ===
<pic-svg>
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.0"
width="200px"
height="200px"
>
<ellipse 
cx="50.0px"
cy="30.0px"
rx="28px" 
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style="fill:yellow;stroke:black;stroke-width:1"
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<g> 
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width="20px"
height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
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height="18.0px"
x="120px"
y="20px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="140px"
y="20px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
<rect 
width="20px"
height="18.0px"
x="160px"
y="20px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
</g> 
<ellipse 
cx="50.0px"
cy="50.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
<rect 
width="20px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="160px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<ellipse 
cx="50.0px"
cy="70.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
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width="20px"
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x="80px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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x="100px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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cx="50.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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width="20px"
height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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width="20px"
height="18.0px"
x="160px"
y="80px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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cx="50.0px"
cy="110.0px"
rx="28px" 
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style="fill:yellow;stroke:black;stroke-width:1"
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<g> 
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<ellipse 
cx="50.0px"
cy="130.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
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width="20px"
height="18.0px"
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y="120px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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width="20px"
height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
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y="120px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
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<ellipse 
cx="50.0px"
cy="150.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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width="20px"
height="18.0px"
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y="140px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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width="20px"
height="18.0px"
x="140px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
x="160px"
y="140px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<ellipse 
cx="50.0px"
cy="170.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
<rect 
width="20px"
height="18.0px"
x="80px"
y="160px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="100px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
x="120px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
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y="160px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="160px"
y="160px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
</g> 
<ellipse 
cx="50.0px"
cy="190.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
<rect 
width="20px"
height="18.0px"
x="80px"
y="180px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
<rect 
width="20px"
height="18.0px"
x="100px"
y="180px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
<rect 
width="20px"
height="18.0px"
x="120px"
y="180px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="140px"
y="180px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
x="160px"
y="180px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
/>
</g> 
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="35px" >
1pass</text>
<rect 
width="20px"
height="18.0px"
x="100px"
y="20px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="35px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="35px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" >
1pass</text>
<rect 
width="20px"
height="18.0px"
x="120px"
y="40px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="55px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" >
2pass</text>
<rect 
width="20px"
height="18.0px"
x="140px"
y="60px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" >
1</text>
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="75px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" >
2pass</text>
<rect 
width="20px"
height="18.0px"
x="160px"
y="80px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" >
1</text>
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="95px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" >
del1</text>
<rect 
width="20px"
height="18.0px"
x="140px"
y="100px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" >
1</text>
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="115px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" >
del2</text>
<rect 
width="20px"
height="18.0px"
x="120px"
y="120px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" >
1</text>
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="135px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="155px" >
rewind</text>
<rect 
width="20px"
height="18.0px"
x="100px"
y="140px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="155px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="175px" >
rewind</text>
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height="18.0px"
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<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="175px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="195px" >
q</text>
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height="18.0px"
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/>
<text x="110.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="195px" >
1</text>
</svg>
</pic-svg>

=== «111» + «1» ===
<pic-svg>
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.0"
width="240px"
height="280px"
>
<ellipse 
cx="50.0px"
cy="30.0px"
rx="28px" 
ry="8px" 
style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
<rect 
width="20px"
height="18.0px"
x="80px"
y="20px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
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<rect 
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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cy="50.0px"
rx="28px" 
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style="fill:yellow;stroke:black;stroke-width:1"
/>
<g> 
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width="20px"
height="18.0px"
x="80px"
y="40px"
style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<rect 
width="20px"
height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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height="18.0px"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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style="fill:none;stroke:#0a14e4;stroke-opacity:1.0000000;"
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<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="255px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="255px" >
1</text>
<text x="50.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="275px" >
q</text>
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width="20px"
height="18.0px"
x="100px"
y="260px"
style="fill:none;stroke:darkblue;stroke-opacity:1.0000000;stroke-width:2px;"
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1</text>
<text x="130.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="275px" >
1</text>
<text x="150.0px" font-family="Tahoma" fontsize="10px" fill="black" text-anchor="middle" y="275px" >
1</text>
</svg>
</pic-svg>


=== «11» + «111» ===
<pic-svg>
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xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
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[[Category:Алгоритмы]]
{{replicate-from-custiswiki-to-lib}}