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, $\\{\\}^\star$?

\[\\{\epsilon\\}\]

Proofs