Determine the state complexity

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Reference no: EM133694933

Question: We start with some definitions. For a string $w \in \Sigma^*$, we define $c(w)$ to be the number of unique symbols in $w$. For example, $c(\epsilon) = 0,$ $c(000) = 1,$ $c(11111) = 1,$ and $c(101) = 2.$ Now let $\Sigma_n$ denote an alphabet with $n$ symbols. Define the language $L_n \subseteq \Sigma_n^*$ as follows. $L_n = \{w \in \Sigma_n^* : c(w) < n\}.$ Determine (with proof) the state complexity of $L_n$ for all $n > 0$. Here, the state complexity of a regular language refers to the minimum number of states in any DFA solving the language.

Reference no: EM133694933

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