If I have DFA accepting
$\{w \in \{a,b\}^*$ s.t. on every odd position in $w$ there is a $b\}$
Would the empty word be accepted? Also, would the word $eb$ be accepted?
1 Answer
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The empty word belongs to the language, since on all its odd positions -- all zero of them -- we find a $b$.
$eb$ does not belong to $\{a,b\}^*$, hence it does not belong to the language.
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$\begingroup$ Why does eb not belong to the language? Apologies if I wasn't clear, I'm denoting the empty word by e. $\endgroup$– user79878Commented Nov 10, 2017 at 22:38
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$\begingroup$ @Leonhard You can simply write it as $b$, then. In such case, it depends on whether "positions" start counting from 1 or from 0. I'd guess from 1 (but it really depends on the convention): if so, that $b$ does belong to the language. $\endgroup$– chiCommented Nov 10, 2017 at 22:44