CPSC 433: Review for Exam 1
Summer 2001

• Lectures through June 20th (through Chomsky and Griebach Normal Forms)

• Readings: Ch 1, Ch 2, Ch 3, Ch 4 (sec 1), Ch 6 (except sec 7), Ch 7 (except sec 7), Ch 5

• Quizzes 1-4 and their solutions (on the course web page)

• Homework assignments 1-3 and their solutions

The format of the exam will be some short answers and some "work-out" problems. Difficulty will be in between the quizzes and the homework (probably leaning more toward the homework). Here are some suggestions for things to know:

• Know the definitions of countably and uncountably infinite and how to use diagonalization to prove a set is uncountable.

• Know how to define a set recursively, how to prove something about the elements of the set inductively, and how recursion and the induction are related.

  Go over the inductive proofs from the homework. Something similar will most likely appear on the exam.

• Know the definition of regular languages and how to represent them using regular expressions.

• Know the definition of a regular grammar.

• Know the definitions of the different kinds of finite automata (deterministic, non-deterministic, with or without lambda transitions). Know the difference in the meaning of language acceptance for deterministic and nondeterministic machines.

• Know how to convert an NFA-lambda to a DFA.

• Know how to convert a regular expression to an NFA-lambda and vice versa.

• Know how to convert a regular grammar into an NFA and vice versa.

• Be able to state the pumping lemma for regular languages.

• Be able to use the pumping lemma to prove that certain languages are not regular.

  Given a DFA (or NFA) and a particular string, be able to trace the computation of the DFA (or computations of the NFA) on the string.

• Know closure properties of regular languages (they are closed under union, concatenation, Kleene star and intersection) and how to use these facts to decide whether or not a language is regular.

• Know the definitions of context-free grammar, parse (derivation) tree, left-most and right-most derivations.

• Know what ambiguous and unambiguous mean in relation to grammars.
• Know definition of Chomsky Normal Form and each of the steps to convert any context-free grammar to Chomsky Normal Form.

• Know the definition of Greibach Normal Form grammar (but not how to convert to it).

• Know the definition of push-down automaton.