Final Concept Review CS60, Fall 1997

There may be a couple of things I've left out, but these seem to be the key points covered in this offering of the course.

General concepts:

• What is a partial function? A function? What do we mean by the "partial function" computed by a program, Turing machine, etc.?
• Relations, directed and undirected graphs
• What is mean by "state"? by "transition"?

Techniques:

• Information structures: lists, trees, trees as lists, lists as trees, graphs
• Use of higher-order functions and predicates, anonymous functions
• Use of recursion
• McCarthy's transformation
• Number representations and encodings, conversion from one to another
• List manipulation in rex and Java
• Difference between [A, B] and [A | B] (list, cons) and append(A, B)
• S expressions, R expressions
• Stacks, queues
• Arrays, linear addressing principle
• Grammars, parsing
• Object-oriented programming
  • Constructors
  • Inheritance
  • Over-riding methods
  • Use of references
  • Static methods
• Proposition logic
  • Truth table, hypercube, and map representations of functions
  • Express one function in terms of others, e.g.
    • 'implies' in terms of 'or', 'not'
    • 'and' in terms of 'or', 'not'
    • 'or' in terms of 'and', 'not'
    • 'iff' in terms of 'or', 'not'
    • 'xor' (exclusive or) in terms of 'or', 'not'
  • Sum-of-products form
  • Simplifying combinational logic expressions
  • Determining whether an expression is a tautology
  • Boole/Shannon expansion
  • Minterm expansion
  • Karnaugh maps
  • Don't cares
• Predicate Logic
  • Meaning of quantifiers
  • Simple logic programming in Prolog
  • Specifying a program
  • Ascertain program correctness
  • Loop invariants
    • Using
    • Proving
  • Energy function for proving termination
• Complexity
  • "O" notation for run-time bounds
  • Simple algorithm analysis (deriving the run-time for a program)
  • Sorting programs
    • Bucket sort
    • Radix sort
    • Quicksort
    • Heap sort
    • Merge sort
  • Empirical analysis
  • Set representations, bit vectors, hashing, etc.
• Finite-State Machines
  • Regular expressions
  • Languages which aren't finite-state
  • Synthesizing a finite-state machine from combinational logic and flip-flops or registers
  • Interconnecting finite-state machines, e.g. parallel connection
• Computer structure
  • Register-transfer level
  • Interpretation of machine instructions
  • Implementation of arrays