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I'm designing a Turing machine that decides a language denoted by a regular expression. Let's say this expression is $a^*bbc^*$. Does this machine accept the string $bb$ since $a^*$ and $c^*$ can have zero instances or more?

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  • $\begingroup$ Yes, $a^*bbc^*$ matches $bb$. $\endgroup$ – Yuval Filmus Oct 24 '14 at 6:25
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    $\begingroup$ The meaning of * is covered in your textbook and in any online reference such as wikipedia. You're expected to do at least basic research before asking here. $\endgroup$ – David Richerby Oct 24 '14 at 8:37
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Yes, the word $bb$ in the language generated by the regular expression $a^*bbc^*$, because, as you say, $a^*$ and $c^*$ generate also the empty word. So if you are building a Turing machine that accepts this language, it should also accept the string $bb$.

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