CS547 Practice Assignment

   February 2005
 S  M Tu  W Th  F  S
       1  2  3  4  5
	     ^assigned
 6  7  8  9 10 11 12
	     ^"due"
13 14 15 16 17 18 19



You are to work in a group of at most 4 people.


If your name appears on an ok completion of this assignment,
AND if you submit non-empty pages throughout the rest of this course,
I guarantee you at least a C- in this course.


You should do this exercise in two different authoring environments.
You should do the same work in each environment, so you can comment
on the difference.  If you use the same tool, such as word, but use
it in a significantly different way each time, then you can say you
have different environments.


Have a person in the group TIME the following exercises.  Also,
if that person can capture an mpeg of a few seconds of the task
being performed, you may report such things as "time fixing editing
errors", "number of times switching from keyboard to mouse", "proportion
of time spent trying to understand what has already been written."


WITHOUT writing the proof in advance (e.g., do not practice on
paper), write the inductive proof of the statement "for all i, a
natural number, the kth power of L set-concatenated with L is equal to
L set-concatenated with L to the kth power."  Obviously you will want
to use symbols here.  You may find that you will want to include
a bit of English text in this proof, and you should "make it look
nice" after you have "authored" it.  So if you want to make the 
layout look a bit nicer, maybe italicize a word here and there, then
you may do so.


Do the same, writing the definition of a FSM.  If you want
to write the definition of the what strings the machine accepts, that's
good, too, but the basic 5-tuple definition suffices.


Now go back to your proof and change L to S, and k to m, and
switch the order of the statement to be proved, so that you are
proving that L L^(k+1) = L^(k+1) L.  Same proof, different ordering
of the symbols.


Go back to your definition and change the 5-tuple to a 4-tuple,
where the start state is pre-defined to be q0.