XDI analysis of Uninitialized Non-Receptive 1-Bit Variable

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME Uninitialized Non-Receptive 1-Bit Variable)
  4>     (SYMBOLS 
  5>       (w0 INPUT) (w1 INPUT) (a OUTPUT) (r INPUT)
  6>       (v0 OUTPUT) (v1 OUTPUT)
  7>     )
  8>     (STATES
  9>       (0 INITIAL BOX)
 10>       (2 TRANSIENT)
 11>       (5 TRANSIENT)
 12>       (1 TRANSIENT)
 13>       (3 BOX)
 14>       (6 BOX)
 15>       (4 TRANSIENT)
 16>       (7 TRANSIENT)
 17>     )
 18>     (TRANSITIONS
 19>       (0 2 w0) (0 5 w1) (0 1 r)
 20>       (2 3 a)
 21>       (5 6 a)
 22>       (1 3 v0) (1 6 v1)
 23>       (3 2 w0) (3 5 w1) (3 4 r)
 24>       (6 2 w0) (6 5 w1) (6 7 r)
 25>       (4 3 v0)
 26>       (7 6 v1)
 27>     )
 28>   )
 29> )
-----------------------------------------------------------------------------

Uninitialized Non-Receptive 1-Bit Variable: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Uninitialized Non-Receptive 1-Bit Variable: 1 warning, 0 errors.

Statistics

6 symbols:

3 input and 3 output

8 states:

0 demanding, 3 indifferent and 5 transient

15 transitions:

9 input and 6 output

Automorphisms (symmetries)

0:	w0	w1	a	r	v0	v1
0:	w1	w0	a	r	v1	v0

Finest Semi-independent Partition

/ w0 w1 a r v0 v1 /

Choice, Order Dependence, Nondeterminism

• Maximally Transient
• Disabling inputs (Z^inp) in state(s):

  0 3 6

• Disabling outputs (Z^out) in state(s):

  1

• Order-Independent input (Y^inp)
• Order-Independent output (Y^out)
• Output refusal sets propate backward over inputs
• Output Non-Deterministic (static)

Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]

	0	2	5	1	3	6	4	7
0:	0	1	1	1	2	2	3	3

Initial state not reachable from 7 states: 2 5 1 3 6 4 7
There are 13 state pairs where one state is unreachable from the other state.

Shortest paths from initial state:

0:
2:	w0
5:	w1
1:	r
3:	w0 a
6:	w1 a
4:	w0 a r
7:	w1 a r

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]

d:	h	[c]
0:	1	[1]
1:	3	[4]
2:	2	[6]
3:	2	[8]

Autocomparison Matrix

There are 4 state pairs (x,y) where x refines y outside the diagonal:

(3[],0[]) (6[],0[]) (4\/,1\/) (7\/,1\/)

XDI Validity

'Uninitialized Non-Receptive 1-Bit Variable' is a valid XDI specification.