Very simple finite automaton (?)

[kpp9c]

Very simple finite automaton (?)

I am not sure if this is and example of Finite Automaton or a Finite
State Machine or perhaps it is related to a transition table or markov
process. I am not a math person so i am not sure what it is called. I
googled around and got lots of super complicated gobbledegoo all with
knotty regex stuff, but what i want to do is much more simple.

I am trying to use a table (called a transition table? i dunno) to
define a bunch of moves like so:

1 --> 2 5
2 --> 1 4
3 --> 3
4 --> 1
5 --> 4 3

so that i can generate a sequence that, given an initial value, will
continue to grow according to these rules.

So starting with 1, we get:

1
2 5
1 4 4 3
2 5 1 1 3
1 4 4 3 2 5 2 5 3


..... etc.

Essentially, iterating over the last added items to the list, applying
the table, adding those new items to the list, applying the table
again... etc, until the sequence reaches some predetermined number of
iterations and quits.


[ [1], [2, 5], [1, 4] , [4, 3], [2, 5], [1], [1], [3], [1, 4], [4, 3],
[2, 5], [2, 5], [3] ]


First, I would like to know what, precisely, this kind of process is
called so that i can look it up. Many names are suggested but when
googling more names and acronyms show up, maybe there are many names
used for a variety of related things, but I could be curious to know
exactly what this is an instance of. Second, I am not sure how to get
started with the loop (is this an example of recursion?) and how best
to represent the table (dictionary)? If anyone has an example of how
to do this or a suggestion on where to start poking around, that would
be great.

cheers,

kp

macosx, python2.5 & 2.6