ONT Re: Zeroth Order Theories (ZOT's)

[Jon Awbrey <jawbrey@oakland.edu>]

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Seth,

I realized after sending that last bunch of bits that there is room
for confusion about what is the input/output of the Study module of
the Theme One program as opposed to what is the input/output of the
"finitely approximated turing automaton" (FATA).  So here is better
delineation of what's what.  The input to Study is a text file that
is known as LogFile(Whatever) and the output of Study is a sequence
of text files that summarize the various canonical and normal forms
that it generates.  For short, let us call these NormFile(Whatelse).
With that in mind, here are the actual IO's of Study, excluding the
glosses in square brackets:

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[Input To Study = FATA Initial Conditions + FATA Program Conditions]

[FATA Initial Conditions For Input 0]

p0_q0

p0_r1

p0_r0_s#
p0_r1_s0
p0_r2_s#

[FATA Program Conditions For Parity Machine]

[Mediate Conditions]

( p0_q#  ( p1_q# ))
( p0_q*  ( p1_q* ))

( p1_q#  ( p2_q# ))
( p1_q*  ( p2_q* ))

[Terminal Conditions]

(( p2_q# )( p2_q* ))

[State Partition]

(( p0_q0 ),( p0_q1 ),( p0_q# ),( p0_q* ))
(( p1_q0 ),( p1_q1 ),( p1_q# ),( p1_q* ))
(( p2_q0 ),( p2_q1 ),( p2_q# ),( p2_q* ))

[Register Partition]

(( p0_r0 ),( p0_r1 ),( p0_r2 ))
(( p1_r0 ),( p1_r1 ),( p1_r2 ))
(( p2_r0 ),( p2_r1 ),( p2_r2 ))

[Symbol Partition]

(( p0_r0_s0 ),( p0_r0_s1 ),( p0_r0_s# ))
(( p0_r1_s0 ),( p0_r1_s1 ),( p0_r1_s# ))
(( p0_r2_s0 ),( p0_r2_s1 ),( p0_r2_s# ))

(( p1_r0_s0 ),( p1_r0_s1 ),( p1_r0_s# ))
(( p1_r1_s0 ),( p1_r1_s1 ),( p1_r1_s# ))
(( p1_r2_s0 ),( p1_r2_s1 ),( p1_r2_s# ))

(( p2_r0_s0 ),( p2_r0_s1 ),( p2_r0_s# ))
(( p2_r1_s0 ),( p2_r1_s1 ),( p2_r1_s# ))
(( p2_r2_s0 ),( p2_r2_s1 ),( p2_r2_s# ))

[Interaction Conditions]

(( p0_r0 ) p0_r0_s0 ( p1_r0_s0 ))
(( p0_r0 ) p0_r0_s1 ( p1_r0_s1 ))
(( p0_r0 ) p0_r0_s# ( p1_r0_s# ))

(( p0_r1 ) p0_r1_s0 ( p1_r1_s0 ))
(( p0_r1 ) p0_r1_s1 ( p1_r1_s1 ))
(( p0_r1 ) p0_r1_s# ( p1_r1_s# ))

(( p0_r2 ) p0_r2_s0 ( p1_r2_s0 ))
(( p0_r2 ) p0_r2_s1 ( p1_r2_s1 ))
(( p0_r2 ) p0_r2_s# ( p1_r2_s# ))

(( p1_r0 ) p1_r0_s0 ( p2_r0_s0 ))
(( p1_r0 ) p1_r0_s1 ( p2_r0_s1 ))
(( p1_r0 ) p1_r0_s# ( p2_r0_s# ))

(( p1_r1 ) p1_r1_s0 ( p2_r1_s0 ))
(( p1_r1 ) p1_r1_s1 ( p2_r1_s1 ))
(( p1_r1 ) p1_r1_s# ( p2_r1_s# ))

(( p1_r2 ) p1_r2_s0 ( p2_r2_s0 ))
(( p1_r2 ) p1_r2_s1 ( p2_r2_s1 ))
(( p1_r2 ) p1_r2_s# ( p2_r2_s# ))

[Transition Relations]

( p0_q0  p0_r1  p0_r1_s0  ( p1_q0  p1_r2  p1_r1_s0 ))
( p0_q0  p0_r1  p0_r1_s1  ( p1_q1  p1_r2  p1_r1_s1 ))
( p0_q0  p0_r1  p0_r1_s#  ( p1_q#  p1_r0  p1_r1_s# ))
( p0_q0  p0_r2  p0_r2_s#  ( p1_q#  p1_r1  p1_r2_s# ))

( p0_q1  p0_r1  p0_r1_s0  ( p1_q1  p1_r2  p1_r1_s0 ))
( p0_q1  p0_r1  p0_r1_s1  ( p1_q0  p1_r2  p1_r1_s1 ))
( p0_q1  p0_r1  p0_r1_s#  ( p1_q*  p1_r0  p1_r1_s# ))
( p0_q1  p0_r2  p0_r2_s#  ( p1_q*  p1_r1  p1_r2_s# ))

( p1_q0  p1_r1  p1_r1_s0  ( p2_q0  p2_r2  p2_r1_s0 ))
( p1_q0  p1_r1  p1_r1_s1  ( p2_q1  p2_r2  p2_r1_s1 ))
( p1_q0  p1_r1  p1_r1_s#  ( p2_q#  p2_r0  p2_r1_s# ))
( p1_q0  p1_r2  p1_r2_s#  ( p2_q#  p2_r1  p2_r2_s# ))

( p1_q1  p1_r1  p1_r1_s0  ( p2_q1  p2_r2  p2_r1_s0 ))
( p1_q1  p1_r1  p1_r1_s1  ( p2_q0  p2_r2  p2_r1_s1 ))
( p1_q1  p1_r1  p1_r1_s#  ( p2_q*  p2_r0  p2_r1_s# ))
( p1_q1  p1_r2  p1_r2_s#  ( p2_q*  p2_r1  p2_r2_s# ))

¤~~~~~~~~~¤~~~~~~~~~¤~~OUTPUT~~¤~~~~~~~~~¤~~~~~~~~~¤

[Output Of Study = FATA Output For Input 0]

 p0_q0
  p0_r1
   p0_r0_s#
    p0_r1_s0
     p0_r2_s#
      p1_q0
       p1_r2
        p1_r2_s#
         p1_r0_s#
          p1_r1_s0
           p2_q#
            p2_r1
             p2_r0_s#
              p2_r1_s0
               p2_r2_s#

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