Transform the NFSA with transition table  XABFSa{}{}{}{F}b{F}{}{A,S}{A,F} and starting state S inta a DFSA and give the transition table of that DFSA. Place the letter X (uppercase) in the top left corner of the matrix. Your states in the first column and inputs in the first row can be in the order of your choice.  The question then offers a 7×3 matrix to be filled in.  Unsure how to transform the NFSA with transition table.  This is my answer but it is incorrect  Im unsure as to what I've done wrong!
Transform the NFSA with transition table  $$\begin{array}{ccc} X&amp;a&amp;b\\ A&amp;\{\}&amp;\{F\}\\ B&amp;\{\}&amp;\{\}\\ F&amp;\{\}&amp;\{A,S\}\\ S&amp;\{F\}&amp;\{A,F\} \end{array}$$  and starting state $S$ inta a DFSA and give the transition table of that DFSA. Place the letter $X$ (uppercase) in the top left corner of the matrix. Your states in the first column and inputs in the first row can be in the order of your choice.  The question then offers a $7\times 3$ matrix to be filled in.  Unsure how to transform the NFSA with transition table.  This is my answer but it is incorrect.  $$\begin{array}{ccc} X&amp;a&amp;b\\ \{S\}&amp;\{F\}&amp;\{A,F\}\\ \{F\}&amp;\{\}&amp;\{A,S\}\\ \{A\}&amp;\{\}&amp;\{F\}\\ \{A,F\}&amp;\{\}&amp;\{A,F,S\}\\ \{A,S\}&amp;\{F\}&amp;\{A,F\}\\ \{A,F,S\}&amp;\{F\}&amp;\{A,F,S\} \end{array}$$
I'm preparing a new template for our students' projects based on memoir. All this projects are supervised (directed) by one or more professors so I would like to declare a command like \author but called \director.   This way the student can declare \director{My professor} and the template will place and format the name.   I would like to be like \author and not just a simple \newcommand because it can include affiliation, several names, etc.  I don't know where is \author declared, where should I look? Showing that every field is an integral domain. How long was Luke Skywalker's training with Yoda? Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero? 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