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Revision difference : standard enumeration |
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| The standard enumeration of \lbrace 0,1\rbrace ^{*} is the sequence of strings $s_0 =\lamda$, $s_1 = 0$, $s_2 = 1$, $s_3 = 00$, $s_4 = 01$, $\cdots$ in lexicographic order. |
The standard enumeration of \lbrace 0,1\rbrace ^{*} is the sequence of strings $s_0 =\lamda$, $s_1 = 0$, $s_2 = 1$, $s_3 = 00$, $s_4 = 01$, $\cdots$ in lexicographic order. |
| The characteristic function of a language $A$ is $\mathcal{X}_{A}:\mathbb{N}\rightarrow \lbrace 0, 1\rbrace$ such that |
The characteristic function of a language $A$ is $\mathcal{X}_{A}:\mathbb{N}\rightarrow \lbrace 0, 1\rbrace$ such that $\mathcal{X}(n)=\begin{cases} |
| \[\mathcal{X}(n)=\begin{cases} |
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| 0,\text{ if }s_n \in A\\ |
0,\text{ if }s_n \in A\\ |
| 1,\text{ if }s_n \notin A |
1,\text{ if }s_n \notin A |
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\end{cases}.\]
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\end{cases}$
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