Final Exam Study Guide
CSE 322: Introduction to Formal Models in Computer Science
Winter 2001

Final Exam, Tuesday March 13, 2001, 2:30-4:20 pm

• Final Exam Policies
  • The final is closed book.
  • An 8 1/2 X 11 inch blue (or green) book is required.
  • You may put your own hand written notes in your blue book to aid you during the exam.
  • The exam begins promptly at 2:30 and ends at 4:20.
• Topics covered
  • Alphabets, strings, and languages. Operations of concatenation and reversal on strings. Operations of union, complement, intersection, concatenation, powering, Kleene star, and reversal on languages.
  • Finite automata. The equivalence of deterministic and nondeterministic finite automata. The subset construction. The cross product construction. Behavioral lemmas and their use. Finding lower bounds on the number of states for certain regular languages.
  • Regular expressions. Regular languages and ways to prove properties about regular languages using induction on regular expression length.
  • Finite automata and regular expressions. Equivalence of finite automata and regular expressions. Finite automata constructions for union, concatenation, Kleene star, complement, and intersection and other operations.
  • Nonregular languages. Direct proofs of nonregular languages using the pigeon hole principle. The pumping lemma for regular languages and its applications.
  • Algorithms for finite state automata. Algorithm for removing e-moves. Polynomial time algorithm for testing membership for NFAs without constructing the equivalent DFA. Algorithms for testing emptiness and finiteness of languages accepted by finite automata.
  • Context-free grammars. Abiguity and Chomsky normal form. Closure properties: union, concatenation, Kleene star, reversal, prefix. Not closed under complement and intersection.
  • Pushdown automata. Equivalence with context-free grammars. Top-down and bottom-up constructions of PDAs from grammars. Deterministic PDAs.
  • Non-context-free languages. The pumping lemma and applications.
  • Turing machines. Equivalence of multitape and single tape Turing machines. Church-Turing thesis. The universal Turing machine.
  • Decidability. The undecidability of the halting problem for Turing machines.
• Study suggestions
  • Do the old final exam in an exam setting.
  • Work in study groups to help each other out in preparation. Give each other problems to do in an exam setting. After doing the problems alone, critique each others answers.
  • Practice each algorithm to improve understanding and accuracy. Creating an equivalent DFA from a NFA. Creating an equivalent regular expression from a NFA. Creating an equivalent NFA from a regular expression. Removing epsilon-transitions. Conversion of grammars to Chomsky normal form. Construction of top-down and bottom-up PDAs from context-free grammars.
  • Review chapters 0, 1, 2, and 3, sections 1-4.
  • Do concrete problems from the book:
    1.12, 1.14, 1.16, 1.17, 1.18, 1.23, 1.31, 1.32, 1.37, 2.4, 2.6, 2.7, 2.14, 2.15, 2.18, 3.8, 3.14, 3.15