Study Guide
CSE 322: Introduction to Formal Models in Computer Science
Autumn 1998

Midterm Exam, November 6, 1998

• Midterm Policies
  • The midterm 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 10:30 and ends at 11:20.
• 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.
  • Regular expressions. Regular languages and ways to prove properties about regular languages using induction on regular expression length.
  • Finite automata. the equivalence of deterministic and nondeterministic finite automata. The subset construction.
  • Finite automata and regular expressions. Equivalence of finite automata and regular expressions. Finite automata constructions for union, concatenation, Kleene star, complement, and intersection. The cross product construction.
  • Nonregular languages. Direct proofs of nonregular languages using the pigeon hole principle. The pumping lemma for regular languages and its applications. Finding lower bounds on the number of states for certain regular languages.
  • Algorithms for finite state automata. Algorithm for removing e-moves. Polynomial time algorithm for testing membership for NFAs. Algorithms for testing emptiness and finiteness of languages accepted by finite automata. Boolean matrices to represent graphs and their use in algorithms for finite state automata. Warshall's algorithm.
  • Context-free grammars. Derivations, leftmost derivations, and parse trees. Ambibuous grammars. Regular languages are also context-free.
• Study suggestions
  • Do the old midterm.
  • Work in study groups to help each other out in preparation
  • Review chapter 1, all sections, chapter 2, all sections except section 2.5, and chapter 3, sections 1 and 2.
  • Do concrete problems from the book:

    1.7- 1.7.4, 1.7.5, 1.7.6	1.8- 1.8.1, 1.8.2, 1.8.3, 1.8.5	2.1- 2.1.1, 2.1.3
    2.2- 2.2.1, 2.2.3, 2.2.9	2.3- 2.3.4, 2.3.7	2.4- 2.4.5, 2.4.8
    2.6- 2.6.2	3.1- 3.1.1, 3.1.2, 3.1,3, 3.1.4	3.2- 3.2.2, 3.2.3, 3.2.4

  • Practice with the techniques we used in class but are not found in the book: showing lower bounds on the number of states needed to accept certain regular languages and using Boolean matrices as an aid in solving problems about finite automata.