Mitderm I Review
Topics to be covered on Midterm I:
 Sets, relations, functions
 Regular Expressions and Regular Languages
 Deterministic Finite Automata
 NonDeterministic Finite Automata
 NonRegular Languages and the Pumping Lemma
 Context Free Grammars
Book Sections to be covered on Midterm I
 Chatper 1, sections 1.11.8
 Chapter 2, sections 2.12.5
 Chapter 3, sections 3.13.2
Sample Questions
 For the language L = all strings over {a,b} that begin and end with aa
 Give a regular expression for L
 Give an NFA (DFA is OK too) for L
 Give an NFA (DFA is OK too) for the complement of L
 Give a regular expression for the complement of L
 For the language L = all strings over {a,b} that contain the substring aa or bb
 Give a regular expression for L
 Give an NFA (DFA is OK too) for L
 Give an NFA (DFA is OK too) for the complement of L
 Give a regular expression for the complement of L
 L = {w : w ∈ (a+b)*, w > 2 and one of the last three symbols in w is a 1}. So, 0010, 0111, 00100, 0101 ∈ L, but 01000 ∉ L

Give a Deterministic Finite Automaton for L
 Give a regular expression for L
 Give a regular expression for the complement of L
 L = all strings over {a,b,c} that contain more a's than c's, and all a's appear before any c's. Thus, aababc, bbabac, aabbc ∈ L, but aca, babacc, and abc ∉ L

Give a ContextFree Grammar for L

Prove that L is not regular
 Relations, partial orders, total orders
 How many different relations R ⊆ A × A are there, in terms of A?
 How many different total orders R ⊆ A × A are there, in terms of A?