# XDI analysis of Initialized bit variable with arbitration

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```Processing AND/IF input stream:
-----------------------------------------------------------------------------
2> (AND/IF_1.0
3> (NFA
4>      (NAME  Initialized bit variable with arbitration)
5>      (INTERPRETATION Verhoeff/XDI)
6>      (NOTE Generated by digg v1.0)
7>      (SYMBOLS
8>               (w0 INPUT)
9>               (w1 INPUT)
10>               (r INPUT)
11>               (v0 OUTPUT)
12>               (v1 OUTPUT)
13>               (a OUTPUT)
14>      )
15>      (STATES
16>         (0 BOX INITIAL)
17>         (1 TRANSIENT)
18>         (2 TRANSIENT)
19>         (3 TRANSIENT)
20>         (4 TRANSIENT)
21>         (5 TRANSIENT)
22>         (6 BOX)
23>         (7 TRANSIENT)
24>         (8 TRANSIENT)
25>         (9 TRANSIENT)
26>         (10 TRANSIENT)
27>         (11 TRANSIENT)
28>         (12 TRANSIENT)
29>         (13 TRANSIENT)
30>         (14 TRANSIENT)
31>         (15 TRANSIENT)
32>         (16 TRANSIENT)
33>         (17 TRANSIENT)
34>      )
35>      (TRANSITIONS
36>          (0 1 w0)
37>          (0 2 w1)
38>          (0 3 r)
39>          (1 4 r)
40>          (1 0 a)
41>          (2 5 r)
42>          (2 6 a)
43>          (3 4 w0)
44>          (3 5 w1)
45>          (3 0 v0)
46>          (4 1 v0)
47>          (4 3 a)
48>          (5 2 v0)
49>          (5 8 v1)
50>          (5 15 a)
51>          (6 7 w0)
52>          (6 8 w1)
53>          (6 9 r)
54>          (7 10 r)
55>          (7 0 a)
56>          (8 11 r)
57>          (8 6 a)
58>          (9 10 w0)
59>          (9 11 w1)
60>          (9 6 v1)
61>          (10 1 v0)
62>          (10 7 v1)
63>          (10 12 a)
64>          (11 8 v1)
65>          (11 9 a)
66>          (12 13 w0)
67>          (12 14 w1)
68>          (12 0 v0)
69>          (12 0 v1)
70>          (13 1 v0)
71>          (13 1 v1)
72>          (13 12 a)
73>          (14 2 v0)
74>          (14 2 v1)
75>          (14 15 a)
76>          (15 16 w0)
77>          (15 17 w1)
78>          (15 6 v0)
79>          (15 6 v1)
80>          (16 7 v0)
81>          (16 7 v1)
82>          (16 12 a)
83>          (17 8 v0)
84>          (17 8 v1)
85>          (17 15 a)
86>      )
87> ))
-----------------------------------------------------------------------------

```

### Statistics

6 symbols:
3 input and 3 output
18 states:
0 demanding, 2 indifferent and 16 transient
50 transitions:
18 input and 32 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Automorphisms (symmetries)

There are 2 automorphisms.
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Finest Semi-independent Partition

/ w0 w1 a / r v0 v1 /
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### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• Disabling inputs (Zinp) in state(s):
0 3 6 9 12 15
• Disabling outputs (Zout) in state(s):
5 10 12 13 14 15 16 17
• Order-Independent input (Yinp)
• Order-Dependent output (Yout) in state(s):
2 7
• Output refusal sets do NOT propagate backward over inputs in state(s):
3 9
• Output Non-Deterministic
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]
11111111
012345678901234567
0:011122233344566344

Initial state reachable from all states.
All states reachable from all other states.

Shortest paths from initial state:
 0: w0 w1 r w0 r w1 r w1 a w1 a w0 w1 r v1 w1 a r w1 a w0 r w1 r v1 r w1 r a w0 a w1 r a w0 a w0 w1 r a w0 a w1 w1 r a w1 r a w0 w1 r a w1

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[ c]
0:11]
1:34]
2:37]
3:4[11]
4:4[15]
5:1[16]
6:2[18]
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### Autocomparison Matrix

There are 16 state pairs (x,y) where x refines y outside the diagonal:
(1\/,7\/) (3\/,12\/) (4\/,10\/) (4\/,13\/) (4\/,16\/) (5\/,14\/) (8\/,2\/) (9\/,15\/) (10\/,16\/) (11\/,5\/) (11\/,14\/) (11\/,17\/) (13\/,10\/) (13\/,16\/) (17\/,5\/) (17\/,14\/)
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### XDI Validity

'Initialized bit variable with arbitration' is a valid XDI specification.

Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

XDI State Graph Tool, Version 2.0 (Feb 17 1998 20:34:43)