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Fixed statement in FAR section #32

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Fixed statement in FAR section #32

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2 changes: 1 addition & 1 deletion deciders/sections/decider-FAR-finite-automata-reduction.tex
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Expand Up @@ -469,7 +469,7 @@ \subsection{Search algorithm: direct FAR algorithm}
& \tag{\ref{far-cond-reject-start}'}
\end{align}

By minimality, a solution of (\ref{far-cond-trailing-0}') and (\ref{far-cond-ass-accepted}') will satisfy (\ref{far-cond-reject-start}') if and only if the minimal solution exhibited above does. Hence, we check (\ref{far-cond-reject-start}') for the minimal $a$ that we constructed and there are two cases:
By minimality, a solution of (\ref{far-cond-trailing-0}') and (\ref{far-cond-ass-accepted}') will satisfy (\ref{far-cond-reject-start}') only if the minimal solution exhibited above does. Hence, we check (\ref{far-cond-reject-start}') for the minimal $a$ that we constructed and there are two cases:

\begin{itemize}
\item If $a$ satisfies (\ref{far-cond-reject-start}') then we have found an NFA satisfying Theorem~\ref{far-main-theorem} and we can conclude that the Turing machine does not halt from the all-0 initial configuration.
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