diff --git a/deciders/sections/decider-FAR-finite-automata-reduction.tex b/deciders/sections/decider-FAR-finite-automata-reduction.tex index 9c92985..d2dd93b 100644 --- a/deciders/sections/decider-FAR-finite-automata-reduction.tex +++ b/deciders/sections/decider-FAR-finite-automata-reduction.tex @@ -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.