Models of Computation MT23, Languages
Flashcards
If $A$ and $B$ are languages, what is $A \cdot B$?
\[A \cdot B = \\{xy : x\in A, y \in B\\}\]
i.e. concatenation.
If $A$ is a language, what is $A^\star$?
\[\\{x _ 1 \cdots x _ k : k \ge 0, x _ i \in A\\} \]
How might you more informally write out $A^\star = \\{x _ 1 \cdots x _ k : k \ge 0, x _ i \in A\\}$?
\[\\{\epsilon\\} \cup A \cup (AA) \cup (AAA) \cup \cdots\]
What is $\varnothing^\star$, or alternatively, $\\{\\}^\star$?
\[\\{\epsilon\\}\]