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--- tanszek:oktatas:techcomm:bn_formulas [2024/10/07 16:22] – created knehez
+++ tanszek:oktatas:techcomm:bn_formulas [2025/11/25 07:50] (current) – knehez
@@ Line 9: / Line 9: @@
 | ''::=''     | definition |
 | ''|''       | alternative |
-| ''{expression}'' | repetition (minimum and maximum repetitions can be specified using subscripts) |
+| \({expression}_{min}^{max}\) | repetition (minimum and maximum repetitions can be specified using subscripts) |
 | ''GOTO''    | terminal symbol (in quotes for clarity, can also use apostrophes instead) |
@@ Line 16: / Line 16: @@
 Let’s start with a few typical examples and try to generalize:
-''ABC-1234, GHT-234, HSD-333, AI-BB-654''
+''ABC-935, GHT-234, HSD-333, AI-BB-654''
 Syntax definition:
 $$
-<license\_plate>::<newType> | <oldType> \\
+<license\_plate>::=<newType> | <oldType> \\
-<oldType>::={<letter>}_3^3 − {<number>}_3^3 \\
+<oldType>::=\{<letter>\}_3^3 − \{<number>\}_3^3 \\
-<newType>::={<letter>}_2^2 − {<letter>}_2^2 − {<number>}_3^3 \\
+<newType>::=\{<letter>\}_2^2 − \{<letter>\}_2^2 − \{<number>\}_3^3 \\
 <letter>::=A|B|C...|Z \\
 <number>::=0|1|2|3|4|5|6|7|8|9 \\
@@ Line 31: / Line 31: @@
 Let’s list a few examples and try to generalize:
-''062012345, +36301234567, 0680460046''
+''062012345, 0036701234567, +36301234567, 0680460046''
+Syntax definition:
+$$
+<phone call>::= \{<prefix>\}_0^1 <city> <customer> \\
+<prefix>::=\{+|00\}_0^1 36|06 \\
+<city>::=\{<number>\}_1^2\\
+<customer>::=\{<number>\}_6^7\\
+<number>::=0|1|2|3|4|5|6|7|8|9 \\
+$$
+=== 3. Example: How can we describe the BNF formula using itself? ===
+\[
+\langle \text{BN formula} \rangle ::= \{\langle \text{rule} \rangle \}_{1}^{\infty}
+\]
+\[
+\langle \text{rule} \rangle ::= \langle \text{identifier} \rangle "::=" \langle \text{expression} \rangle
+\]
+\[
+\langle \text{identifier} \rangle ::= "\langle" \langle \text{letter} \rangle \mid \left\lbrace \langle \text{letter} \rangle \mid \langle \text{digit} \rangle \right\rbrace "\rangle"
+\]
+\[
+\langle \text{expression} \rangle ::= \langle \text{term} \rangle \left\lbrace "|" \langle \text{term} \rangle \right\rbrace
+\]
+\[
+\langle \text{term} \rangle ::= \langle \text{factor} \rangle \left\lbrace \langle \text{factor} \rangle \right\rbrace
+\]
+\[
+\langle \text{factor} \rangle ::= \langle \text{identifier} \rangle \mid \langle \text{terminal_symbol} \rangle
+\]
+\[
+\langle \text{terminal_symbol} \rangle ::= \left\lbrace \langle \text{character} \rangle \right\rbrace
+\]
+\[
+\langle \text{letter} \rangle ::= \langle \text{uppercase} \rangle \mid \langle \text{lowercase} \rangle
+\]
+\[
+\langle \text{uppercase} \rangle ::= A \mid B \mid C \dots Z
+\]
+\[
+\langle \text{lowercase} \rangle ::= a \mid b \mid c \dots z
+\]
+\[
+\langle \text{digit} \rangle ::= 0 \mid 1 \mid 2 \mid 3 \mid 4 \mid 5 \mid 6 \mid 7 \mid 8 \mid 9
+\]