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@@ -105,6 +105,7 @@ Formal languages are classified into four nested levels:
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#definition[
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A _decision problem_ is a question with a "yes" or "no" answer depending on the input.
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Formally, the set of inputs for which the answer is "yes" forms a language $L subset.eq Sigma^*$.
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_Deciding_ the problem = _recognizing_ the language $L$.
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#Block(color: yellow)[
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"Is $w in L$?" and "does the algorithm say yes on input $w$?" are _the same question_.
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Formal language theory gives us the mathematics to study the _limits of computation_.
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