Problem 3. Consider the following definition fun f(a : int,b,c) a + b[c(a)] (c) = using Hindley-Milner type inference, determine the type of f. def f(a: int,b,c) + a apply b apply a

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.

For each of the following regular expressions over Σ = {a, b}, state 5 strings that are in the language of the regular expression, and 5 strings that are not.  1. (a∗b)∗|a∗2. (Σ∗aaΣ∗)|(Σ∗bbΣ∗)|(ab)∗|(ba)∗|a|b

Build a deterministic FA Ma such that L= L(Ma) = a((a+b)(a+b))*b For example, baba e La and aab e L4, but ab e La and abaaab e La.