88 lines
2.4 KiB
Markdown
88 lines
2.4 KiB
Markdown
```
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date: 20221205115525
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```
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# Notacja Chomsky'ego:
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$G=<V,\Sigma,P,\sigma>$, gdzie:
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- V - symbole terminalne
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- $\Sigma$ - metaalfabet - alfabet pomocniczy - symbole pomocnicze
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- P - lista produkcji
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- $\sigma$ - Głowa gramatyki
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abc
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aaaabcccccc
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aabbbc
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## $\begin{gathered}a^{n}b^{m}c^{k} &n,m,k\geqslant1\end{gathered}$
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$G_{1}=<V_1,\Sigma_1,P_1,\sigma_1>$
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$V_1 = \{a,b,c\}$
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$\Sigma_1=\{\alpha,\beta,\gamma\}$
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$P_1=\begin{cases}\alpha \rightarrow a\alpha \\ \alpha \rightarrow a\beta \\ \beta \rightarrow b\beta \\ \beta \rightarrow b\gamma \\ \gamma \rightarrow c\gamma \\ \gamma \rightarrow c \end{cases}$
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$\sigma_1 = \alpha$
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## $\begin{gathered}a^{n}b^{m}c^{n} &n,m\geqslant1\end{gathered}$
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$G_{2}=<V_2,\Sigma_2,P_2,\sigma_2>$
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$V_2 = \{a,b,c\}$
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$\Sigma_2=\{\alpha,\beta\}$
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$P_2=\begin{cases}\alpha \rightarrow a\alpha c \\ \alpha \rightarrow a\beta c \\ \beta \rightarrow b \beta \\ \beta \rightarrow b \end{cases}$
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$\sigma_2 = \alpha$
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## $\begin{gathered}a^{n}b^{n}c^{n} &n\geqslant 1 \end{gathered}$
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$G_{3}=<V_2,\Sigma_2,P_2,\sigma_2>$
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$V_3 = \{a,b,c\}$
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$\Sigma_3=\{\alpha,\beta\}$
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$P_3=\begin{cases}\alpha \rightarrow abc \\ \alpha \rightarrow a\alpha \beta c \\ b\beta \rightarrow bb \\ c\beta \rightarrow \beta c \end{cases}$
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$\gamma = \alpha$
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## Przykłady
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abbccc w $G_1$
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$\alpha \rightarrow^2 a\beta \rightarrow^3 ab\beta \rightarrow^4 abb\gamma \rightarrow^5 abbc\gamma \rightarrow^5 abbcc\gamma \rightarrow^6 abbccc$
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Drzewo gramatyki
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```
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abbccc
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||||||
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|||||γ
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||||γ
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|||γ
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||β
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|β
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α
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```
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aaabbbccc $a^nb^nc^n$
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$\alpha \rightarrow^2 a\alpha\beta c \rightarrow^2aa\alpha\beta c\beta c\rightarrow^1 aaabc\beta c\beta cc \rightarrow^{4,4} aaab\beta c\beta cc \rightarrow^4 aaab\beta\beta cc \rightarrow^3 aaabb\beta ccc\rightarrow^3 aaabbbccc$
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# Notacja BNF:
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$V={a,b,c}$
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$\Sigma = \{<\alpha>,<\beta>\}$
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$P = \begin{gathered}\{<\alpha>::= a<\alpha>c|a<\beta>c \\ <\beta>::= a \}\end{gathered}$
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b
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### Nazwy zmiennych:
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$$\begin{gathered}
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V=\{a..z,A..Z,0..9\} \\
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\Sigma = \{<ident>,<litera>,<cyfra>\} \\
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P=\{<ident>::=<litera>|<ident><litera>|<ident><cyfra>\\
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<ident>::=a|..|z|A|..|Z \\
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<cyfra>::=0|..|9 \} \\
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\sigma = <ident>
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\end{gathered}$$
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### Adres IP
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V={0..9,.}
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Σ = {<IP>, <bajt>, <l1>,<l2>,<l3>, <0-9>
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P={<IP>::=<bajt>.<bajt>.<bajt>.<bajt>
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<bajt>::=<l1>|<l2>|<l3>
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<l1>::=<0-9>
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<0-9>::=0|<1-9>
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<l2>::=<1-9><0-9>
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<1-9>::=1|..|9
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<l3>::=1<0-9><0-9>|2<0-4><0-9>|25<0-5>
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<0-4>::=0|1|2|3|4
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<0-5>::=5|<0-4>}
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σ=<IP> |