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46 |
47 \item Given the regular expression $r = (a \cdot b + b)^*$. |
47 \item Given the regular expression $r = (a \cdot b + b)^*$. |
48 Compute what the derivative of $r$ is with respect to |
48 Compute what the derivative of $r$ is with respect to |
49 $a$, $b$ and $c$. Is $r$ nullable? |
49 $a$, $b$ and $c$. Is $r$ nullable? |
50 |
50 |
51 \item Prove that for all regular expressions $r$ we have |
51 \item (Moved to HW3) |
52 |
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53 \begin{center} |
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54 $\textit{nullable}(r) \quad \text{if and only if} |
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55 \quad [] \in L(r)$ |
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56 \end{center} |
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57 |
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58 Write down clearly in each case what you need to prove |
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59 and what are the assumptions. |
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60 |
52 |
61 \item Define what is meant by the derivative of a regular |
53 \item Define what is meant by the derivative of a regular |
62 expressions with respect to a character. (Hint: The |
54 expressions with respect to a character. (Hint: The |
63 derivative is defined recursively.) |
55 derivative is defined recursively.) |
64 |
56 |