equal
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36 |
36 |
37 |
37 |
38 \noindent |
38 \noindent |
39 where $\Sigma^*$ is in our case the set of all strings (what follows in this section |
39 where $\Sigma^*$ is in our case the set of all strings (what follows in this section |
40 also holds for any kind of ``domain'', like the set of all integers or |
40 also holds for any kind of ``domain'', like the set of all integers or |
41 the set of all binary trees, etc). Let us assume $P(s)$ is a property that |
41 the set of all binary trees, etc).\footnote{NOTE: In the videos and slides I use \textit{UNIV} as notation for $\Sigma^*$. } Let us assume $P(s)$ is a property that |
42 is about strings, for example $P(s)$ could be ``the string $s$ has |
42 is about strings, for example $P(s)$ could be ``the string $s$ has |
43 an even length'', or ``the string $s$ starts with the letter |
43 an even length'', or ``the string $s$ starts with the letter |
44 \texttt{a}''. Every such property carves out a subset of strings from |
44 \texttt{a}''. Every such property carves out a subset of strings from |
45 $\Sigma^*$, which in the picture above is depicted as a grey |
45 $\Sigma^*$, which in the picture above is depicted as a grey |
46 circle. This subset of strings is often written as a comprehension like |
46 circle. This subset of strings is often written as a comprehension like |