Day 27, Mat385

• The Zooms continue

  A menu of our past zooms...

• Homework:
  • 8.1: #1, 10, 12

    I put my solutions up with the caveat that I didn't add the reasons for my steps. Consider it an exercise to the reader to fill those in...:) I may have also combined a few steps at once.

    A few of you had solutions more elegant than mine. Kudos to you if you found one!

  • 8.2: #11, 22, 29

• I hope that you're working on your projects!

  Eric emailed, and got his login restored. Others?

  I know that some of you didn't get your logins for the wiki. When you're ready email me and I'll activate it. That way we'll know that it's just been sent out.

• We finished Section 8.2: Logic Networks, in which we saw three different ways of thinking about the same problem: a truth table, a Boolean expression, and a logic network.

• Then it was on to Section 8.3: Minimization.

• Today we start Section 9.3: Finite-State Machines.

  I've made a handout, so that you can play along.

• I love FSMs, and have implemented them in lisp, etc. But I was using some compartmental modeling software for my math modeling class, and realized that we could use that for building a little FSM. So I thought that I'd make something useful -- the binary adder.

  So if you want to try the binary adder I created, here ya go. And it's easy enough to build other little machines (but there are certain pains, because we're using a tool which really wasn't intended for this...:)

  1. You can get a free account on InsightMaker (but you won't need it to just run my examples).

  2. Open up My binary adder FSM at InsightMaker. If you have an account you can "Clone" it (upper right) -- then you'll own your own copy (and can change it to make your own FSM, or give your own input).

  3. You need to make two changes: set the two binary numbers' values, and then within "Settings" you need to set the length of the simulation. Then "Simulate" will run the machine, and generate the sum.

  4. I wrote this little bit of code to create the input in the right form:

     This writes the input vectors for random integers (with padding), and tells what settings to fix, etc. Also the expected output, so one can confirm that the machine is working....

  5. The instructions are included in the insight, at right. I've made a little video to illustrate how it works -- to walk you through it. Take a stroll, if you like!:)

  6. I built a little FSM to do the recognition of Exercise 26b, p. 754 -- set of all strings where the number of 0s is a multiple of 3.

This was fun to program, but probably more trouble than it was worth. A direct approach, as in my implementation of Bellman-Ford below, would have been simpler to code. But, if I can do something recursively, I probably will...:)

• Supplementary Material On-line

If you check out this code, you'll see where I compute the power set ("all-subsets") of a set, to cover all the bases. I think that the end result is pretty beautiful, too!

1. Simple and clean recursive Euclidean Algorithm in lisp:
2. Written as a while loop, using the recurrence relation: