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% Document Info
\author{Vipera}
\pdfinfo{
  /Title (automata-turing-machines.pdf)
  /Creator (Cheatography)
  /Author (Vipera)
  /Subject (Automata - Turing Machines Cheat Sheet)
}

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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Automata - Turing Machines Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Vipera} via \textcolor{DarkBackground}{\uline{cheatography.com/128346/cs/25685/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Vipera \\
  \uline{cheatography.com/vipera} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 13th December, 2020.\\
   Updated 13th December, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Turing Machine Basics}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Transitions are in form: {\bf{a→b,L}}\{\{nl\}\}meaning read a, write b, move left} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Accept input if machine halts in an accept state} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Reject input if machine halts  in a non-accept state {\bf{or}} machine enters  an infinite loop} \tn 
% Row Count 5 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Turing Machines Definition}}  \tn
% Row 0
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Turing Machine: & M = (Q,Σ,Γ,δ,q0,◊,F) \tn 
% Row Count 2 (+ 2)
% Row 1
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{\bf{Q}}: States & \{q0,q1,q2\} \tn 
% Row Count 3 (+ 1)
% Row 2
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{\bf{Σ}}: Input Alphabet & \{a,b\} \tn 
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% Row 3
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{\bf{Γ}}: Tape Alphabet & \{a,b\} \tn 
% Row Count 6 (+ 1)
% Row 4
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{\bf{δ}}: Transition functions & δ(q1,c)=(q2,d,L) \tn 
% Row Count 8 (+ 2)
% Row 5
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\mymulticolumn{2}{x{5.377cm}}{{\bf{q0}}: Initial state} \tn 
% Row Count 9 (+ 1)
% Row 6
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\mymulticolumn{2}{x{5.377cm}}{{\bf{◊}}: Blank} \tn 
% Row Count 10 (+ 1)
% Row 7
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{\bf{F}}: Accept States & \{q2\} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Deciders}} are Turing Machines that halt on all strings: always either accept or reject an input, never loop (infinitely) \newline {\bf{Recognizers}} are Turing Machines that will halt and accept the strings in the language and either reject or do not halt for strings not in the language}  \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Computing Functions with TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Use unary (number represented as 1s {\emph{e.g. 5=11111}})} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Initial and Final configurations are at the begining of the tape} \tn 
% Row Count 4 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Stay-Option TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Head can move Left, Right or Stay} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Stay-Option machines simulate Standard Turing machines (just dont use the stay)} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Standard Turing machines simulate Stay-Option machines: just change the Stay transitions from\{\{nl\}\}a→b,S to \{\{nl\}\}a→b,L and x→x,R where x∈Γ} \tn 
% Row Count 6 (+ 3)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Semi-Infinite Tape TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{The head extends infinitely only to the right} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Standard Turing machines simulate Semi-Infinite machines\{\{nl\}\}Insert special symbol \# on the left of the input string and add a selfloop to every state of \#→\#,R} \tn 
% Row Count 5 (+ 4)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Semi-Infinite tape machines simulate Standard Turing machines: Squeeze infinity of both directions in one direction} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Multi-Tape TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Input string appears on Tape 1, but both tapes are read/write} \tn 
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% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Transitions are in form: (b, f ) →(g,d),L,R} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Multi-tape machines simulate standard Turing Machines: The second one just remains empty} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Standard Turing machines simulate  Multi-tape machines: Uses a multi-track tape to simulate  the multiple tapes} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Multidimensional TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{For example 2-dimensional tape, has moves L,R,U,D (Up, down) and position of x and y} \tn 
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% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Multidimensional machines simulate  Standard Turing machines: only use 1 dimension} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Standard Turing machines simulate  Multidimensional machines: Two tape machine\{\{nl\}\}•One tape with two tracks (symbols in track 1, coordinates in track 2)\{\{nl\}\}•Second tape for current coordinates} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Nondeterministic TM}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{Nondeterministic machines simulate  Standard (deterministic) Turing machines} \tn 
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% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Standard (deterministic) Turing machines  simulate Nondeterministic machines:\{\{nl\}{]}•Use a 2D Tape\{\{nl\}\}•Store all possible computations of the non-deterministic machine on the 2D Tape} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}