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\section*{Homework 3}

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\item Assume you have an alphabet consisting of the letters $a$, $b$ and $c$ only.

(a) Find a regular expression that recognises the two strings $ab$ and $ac$. (b)

Find a regular expression that matches all strings \emph{except} these two strings.

Note, you can only use regular expressions of the form 

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$r ::= \varnothing \;|\; \epsilon \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$

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\item Define the function $zeroable$ which takes a regular expression as argument

and returns an integer. The function should satisfy the following property:

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$zeroable(r)$ \;if and only if\; $L(r) = \varnothing$

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