# XDI analysis of Nacking Arbiter

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

```Processing AND/IF input stream:
-----------------------------------------------------------------------------
1> (AND/IF_1.0
2>   (NFA
3>     (NAME Nacking Arbiter)
4>     (INTERPRETATION Verhoeff/XDI)
5>     (SYMBOLS
6>       (r0 INPUT) (a0 OUTPUT) (n0 OUTPUT) (r1 INPUT)
7>       (a1 OUTPUT) (n1 OUTPUT)
8>     )
9>
10>     (STATES
11>       (0 INITIAL BOX)
12>       (1 TRANSIENT)
13>       (4 TRANSIENT)
14>       (2 BOX)
15>       (5 TRANSIENT)
16>       (1.1 TRANSIENT)
17>       (5.1 TRANSIENT)
18>       (1.2 TRANSIENT)
19>       (5.4 TRANSIENT)
20>       (3 TRANSIENT)
21>       (6 TRANSIENT)
22>       (7 TRANSIENT)
23>       (3.1 TRANSIENT)
24>       (7.1 TRANSIENT)
25>       (8 BOX)
26>       (4.1 TRANSIENT)
27>       (5.2 TRANSIENT)
28>       (4.2 TRANSIENT)
29>       (5.3 TRANSIENT)
30>       (9 TRANSIENT)
31>       (10 TRANSIENT)
32>       (11 TRANSIENT)
33>       (12 TRANSIENT)
34>       (14.0 TRANSIENT)
35>       (11.1 TRANSIENT)
36>       (12.1 TRANSIENT)
37>       (13 TRANSIENT)
38>       (14.1 TRANSIENT)
39>     )
40>     (TRANSITIONS
41>       (0 1 r0) (0 4 r1)
42>       (1 2 a0) (1 5 r1)
43>       (4 5 r0) (4 8 a1)
44>       (2 3 r0) (2 6 r1)
45>       (5 6 a0) (5 4.1 n0) (5 9 a1) (5 1.1 n1)
46>       (1.1 2 a0) (1.1 5.1 r1)
47>       (5.1 6 a0) (5.1 1.1 n1)
48>       (1.2 2 a0) (1.2 0 n0) (1.2 5.4 r1)
49>       (5.4 6 a0) (5.4 4 n0) (5.4 9 a1) (5.4 1.1 n1)
50>       (3 0 a0) (3 7 r1)
51>       (6 7 r0) (6 2 n1)
52>       (7 4.2 a0) (7 10 a1) (7 3 n1)
53>       (3.1 0 a0) (3.1 7.1 r1)
54>       (7.1 4 a0) (7.1 10 a1)
55>       (8 9 r0) (8 11 r1)
56>       (4.1 5.2 r0) (4.1 8 a1)
57>       (5.2 4.1 n0) (5.2 9 a1)
58>       (4.2 5.3 r0) (4.2 8 a1) (4.2 0 n1)
59>       (5.3 6 a0) (5.3 4.1 n0) (5.3 9 a1) (5.3 1 n1)
60>       (9 8 n0) (9 12 r1)
61>       (10 8 a0) (10 14.0 r1)
62>       (11 12 r0) (11 0 a1)
63>       (12 13 a0) (12 11 n0) (12 1.2 a1)
64>       (14.0 11 a0) (14.0 3.1 a1)
65>       (11.1 12.1 r0) (11.1 0 a1)
66>       (12.1 13 a0) (12.1 1 a1)
67>       (13 14.1 r0) (13 2 a1)
68>       (14.1 11.1 a0) (14.1 3 a1)
69>     )
70>   )
71> )
-----------------------------------------------------------------------------

```

### Statistics

6 symbols:
2 input and 4 output
28 states:
0 demanding, 3 indifferent and 25 transient
66 transitions:
20 input and 46 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

/ r0 a0 n0 / r1 a1 n1 /
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Zinp)
• Disabling outputs (Zout) in state(s):
5 1.2 5.4 7 4.2 5.3 12
• Order-Independent input (Yinp)
• Order-Dependent output (Yout) in state(s):
3 11
• Output refusal sets do NOT propagate backward over inputs in state(s):
1 4 6 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
0142515153673784545901241234
....   .. ....    ... .
1124   11 1223    011 1
0  :0112234563347823456353467856

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

Shortest paths from initial state:
 0  : r0 r1 r0 a0 r0 r1 r0 r1 n1 r0 r1 n1 r1 r0 r1 a1 r1 a1 r0 r1 a1 r1 a1 r1 r0 a0 r0 r0 a0 r1 r0 a0 r0 r1 r0 a0 r0 r1 a1 r1 a1 r0 a0 r0 r1 a1 r1 a1 r1 r1 a1 r0 r1 n0 r0 r1 n0 r0 r0 a0 r0 r1 a0 r0 a0 r0 r1 a0 r0 r0 r1 a1 r0 a0 r0 r1 a1 r1 a1 r1 r0 r1 a1 r1 r0 a0 r0 r1 a1 r1 r0 r1 a1 r1 a0 r0 a0 r0 r1 a1 r1 a0 r0 a0 r0 r0 r1 a1 r1 a0 r0 r1 a1 r1 a0 r0

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[ c]
0:11]
1:23]
2:36]
3:6[12]
4:4[16]
5:4[20]
6:4[24]
7:2[26]
8:2[28]
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Autocomparison Matrix

There are 18 state pairs (x,y) where x refines y outside the diagonal:
(1\/,1.2\/) (4\/,4.2\/) (5\/,5.4\/) (5\/,5.3\/) (1.1\/,1\/) (1.1\/,1.2\/) (5.1\/,5\/) (5.1\/,5.4\/) (5.1\/,5.3\/) (3.1\/,3\/) (7.1\/,7\/) (4.1\/,4\/) (4.1\/,4.2\/) (5.2\/,5\/) (5.2\/,5.4\/) (5.2\/,5.3\/) (11.1\/,11\/) (12.1\/,12\/)
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### XDI Validity

'Nacking Arbiter' 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)