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Josip Deak

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\Large{ \textbf{zadatak $3$\ }}\\[1mm]
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Za zadani DKA M (slika!!): \\
\quad (a) \quad odredite RI rje\v{s}avanjem pripadnih skupovnih jednad\v{z}bi \\
\quad (b) \quad konstruirajte ekvivalentni NKA N
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    \begin{center}Slika 1. \emph{DKA M}
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\underline{\textbf{Rj:}} \\
 (a) \\
 \begin{tabular}{p{7cm}}
 $X=0X+1Y$ \qquad \qquad \qquad \qquad$(1)$ \\
 $Y=1X+0Z+\varepsilon$ \ \qquad \qquad \qquad $(2)$ \\
 $Z=0X+1Y$ \qquad \qquad \qquad \qquad $(3)$ \\
 \hrule

 $Y=1X+0(0X+1Y)+\varepsilon$ \quad$(3)\rightarrow(2)$ \\
 $Y=1X+00X+01Y+\varepsilon$ \\
 $Y=01Y+1X+00X+\varepsilon$ \\
 $Y=(01)^{*} (1X+00X+\varepsilon)$ \\
 \hrule

 $X=0X+1(01)^{*}(1X+00X+\varepsilon)$ \\
 $X=0X+1(01)^{*}1X+1(01)^{*}00X+1(01)^{*}\varepsilon$ \\
 $X=(0+1(01)^{*}1+1(01)^{*}0)X + 1(01)^{*}\varepsilon$ \\
 $X=(0+1(01)^{*}1+1(01)^{*}0)^{*} 1(01)^{*}$ \\
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(b) \\
 \qquad $\Rightarrow$ Budu\v{c}i je DKA $\subseteq$ NKA gore navedeni DKA je ujedno i NKA $\checkmark$
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 \begin{description} \item[nap]: \\
 \qquad \small{ To\v{c}no rije\v{s}en zadatak nosi $15$(a)+$5$(b) bodova   }
 \end{description}
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