theocs:lecture3

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theocs:lecture3 [2024/10/10 12:15] – created tamitheocs:lecture3 [2024/10/10 12:22] (current) – tami
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 $$(-+\Lambda) D D^{\ast} (\Lambda+.D^{\ast}), D \ \text{stands for digit}$$ $$(-+\Lambda) D D^{\ast} (\Lambda+.D^{\ast}), D \ \text{stands for digit}$$
  
 +Basis:
 $$\emptyset, \{\Lambda\} \text{ and } \{a\} \text{ are regular languages for all } a \in \Sigma$$ $$\emptyset, \{\Lambda\} \text{ and } \{a\} \text{ are regular languages for all } a \in \Sigma$$
 +
 +The basis of the definition gives us the following for regular languages over the alphabet $\Sigma = \{a,b\}$
 +
 +**All** regular languages $\Sigma$ can be built from combining these four in various ways by **recursively using the union, product and closure operation**.
 +
 +  * $\{\Lambda,b\}$ is regular: $\{\Lambda\} \cup \{b\} = \{\Lambda, b\}$
 +
 +Any finite languages is easy to build in this way $\implies$ **All finite languages are regular!**
  • theocs/lecture3.1728562533.txt.gz
  • Last modified: 2024/10/10 12:15
  • by tami