CS 311 MIDTERM TOPICS


DEFINITIONS

Formal Language
Deterministic Finite Automaton (DFA)
Acceptance and recognition by a DFA
Regular Language
Regular Grammar
Nondeterministic Finite Automaton (NFA)
Acceptance and recognition by a NFA
Regular Expressions -- Syntax and Meaning
Context-free Grammar (CFG)
Derivation in a CFG
Context-free Language
Ambiguity in CFGs
Pushdown Automaton (PDA)
Acceptance and Recognition by a PDA

THEOREMS

(You should be able to state and apply
these theorems, and, except as noted,
outline their proofs.)

Equivalence of DFAs and NFAs.
Equivalence of DFAs and Regular Expressions.
Closure of Regular Languages under 
   union, concatenation, Kleene-*,
   intersection, complement.
Pumping Lemma for Regular Languages.
Closure of CFLs under union, concatenation, Kleene-*
Equivalence of PDAs that accept by Empty Stack and by Final state
Equivalence of CFLs and PDAs
Pumping Lemma for CFLs

TASKS

Design a simple DFA, NFA, regular expression, CFG, or PDA
  from an informal language description.
Give an informal language desrcription for a simple DFA, NFA,
  regular expression, CFG, or PDA.
Apply simple equivalence laws for rewriting regular expressions.
Apply the union, concatenation, or Kleene-* construction on NFAs
Apply the product and complement constructions to DFAs.
Perform the subset construction for converting an NFA to a DFA,
  including computing epsilon-closures.
Construct an NFA from a regular expression.
Construct a regular expression from a DFA (either method)
Prove a language to be non-regular by applying the pumping lemma
  andr the closure laws.
Apply the union, concatenation, or Kleene-* operators on CFGs.
Give a paper simulation of the behavior of a DFA, NFA, or PDA
  on a specified input.
Prove a language to be non-Context-free by applying the pumping lemma and the closure laws


EXAMPLES

You should be familiar with standard examples and non-examples
of regular and context-free languages.