Regular Language

languages

Definition

Regular Language

A language is called regular if all words in the language are formed by unity, concatenation or star exponent.

Operations

Unity

$$\{a,b,\dots \}\cup \{c,d,\dots \}=\{a,b,\dots ,c,d,\dots \}$$

Concatenation

$$\{a,b,\dots \}\cdot \{c,d,\dots \}=\{ac,ad,\dots ,bc,bd,\dots \}$$

Exponents

$$\begin{array}{rl}{L}^0& =\{\epsilon \}\\ L^1& =L\cdot L^0=L\\ L^n& =L^0\cdot L^1\cdot \dots \cdot L^n\end{array}$$

Star

$$L^{\ast }=\bigcup _{n\ge 0}{L}^n$$

Plus

$$L^{+}=\bigcup _{n\ge 1}{L}^n$$