Problem 1 Draw the 5-tuple representing the machine

Problem 2 Draw (with paper and pencil) the machine represented by the five-tuple: \[ \left( \{1,0,x\}, \{a,b,c\}, {\small \begin{array}{c|ccc} &a&b&c\\ \hline% 1&1&1&0\\ 0&1&x&x\\ x&x&x&x \end{array}}, 1, \{1,0\} \right) \]

Problem 4 Consider the following function (recall that Σ* denotes the set of all strings over alphabet Σ, λ denotes the empty string, and N denotes the non-negative integers) and give the values of each of the following expressions, or "error" if the function's argument is outside of its domain:

f:{a,b}* → N
f(w) = 2|w|

• f(aab)
• f(acab)
• f(λ)

Problem 3 Consider the following function (recall that Z denotes the integers and N denotes the non-negative integers) and give the values of each of the following expressions, or "error" if the function's argument is outside of its domain:

f:N x Z → Z
f(a,b) = a - b

• f(-2,3)
• f(0)
• f(2,-7)