CS 311 FINAL EXAM TOPICS

The final exam will be comprehensive over the entire course.
Thus, this list includes all the topics listed for the midterm.
The horizontal lines separate pre- and post- midterm topics.


DEFINITIONS

Formal Language
Deterministic Finite Automaton (DFA)
Acceptance and recognition by a DFA
Regular Language
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
Ambiguity in Languages
Pushdown Automaton (PDA)
Acceptance and Recognition by a PDA
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Chomsky Normal Form (CNF)
Turing Machine (TM)
Recognition and Decision by a TM
Computability of a function by a TM
Multitape TM
Nondeterministic TM (NTDM)
Church-Turing Thesis
Lambda-calculus
PDA with k stacks (k-PDA)
k-Counter machines
Universal Turing Machine (U)
Reduction
Time Complexity class (TIME)
Space Complexity class (SPACE)
Class P
Class NP
Poynomial-time reduction
NP-Complete

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 CFGs and PDAs 
----------------------------------------------
Pumping Lemma for CFLs
Equivalence of ordinary TM, semi-infinite tape TM, multitape TM, NDTM, 2-PDA, and 2-counter machine.
Existence of a Turing-undecidable language.
Existence of a Turing-unrecognizable language.
Equivalence of lambda-calculus and TM. (no proof).
Equivalence of unrestricted grammar and TM (no proof).
Equivalence of partial recursive functions and lambda-caculus (no proof).
SAT is NP-complete (no proof)

TASKS

Design a simple DFA, NFA, regular expression, CFG, or PDA
  from an informal language description.
Give an informal language description 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
  and/or 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.
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Calculate the CNF of a CFG.
Prove a language to be non-context-free by applying the pumping
  lemma and/or the closure laws.
Give a paper simulation of the behavior of a TM on a specified input.
Design a simple TM to recognize or decide an informal language 
 description.
Prove undecidability of a language using reduction.
Manipulate big-O notation.

I will *not* ask you to show that a language is NP-complete.

EXAMPLES

You should be familiar with standard examples and non-examples
of regular, context-free, Turing-acceptable, Turing-decidable, 
Turing-undecidable, non-Turing-acceptable, P, NP, and NP-complete languages.

You should know the basic inclusion relationships among the classes:
regular languages, context-free languages, P, NP, Turing-decidable
languages, Turing-recognizable languages.