# XDI analysis of RGD 1-arbiter

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```Processing AND/IF input stream:
-----------------------------------------------------------------------------
2> (AND/IF_1.0
3> (NFA
4>      (NAME RGD 1-arbiter)
5>      (INTERPRETATION Verhoeff/XDI)
6>      (NOTE Generated by digg v1.0)
7>      (SYMBOLS
8>               (r0 INPUT)
9>               (r1 INPUT)
10>               (d INPUT)
11>               (g0 OUTPUT)
12>               (g1 OUTPUT)
13>      )
14>      (STATES
15>         (0 BOX INITIAL)
16>         (1 TRANSIENT)
17>         (2 TRANSIENT)
18>         (3 TRANSIENT)
19>         (4 BOX)
20>         (5 BOX)
21>         (6 BOX)
22>         (7 BOX)
23>      )
24>      (TRANSITIONS
25>          (0 1 r0)
26>          (0 2 r1)
27>          (1 3 r1)
28>          (1 4 g0)
29>          (2 3 r0)
30>          (2 4 g1)
31>          (3 5 g0)
32>          (3 6 g1)
33>          (4 6 r0)
34>          (4 5 r1)
35>          (4 0 d)
36>          (5 7 r0)
37>          (5 2 d)
38>          (6 7 r1)
39>          (6 1 d)
40>          (7 3 d)
41>      )
42> ))
-----------------------------------------------------------------------------

```

### Statistics

5 symbols:
3 input and 2 output
8 states:
0 demanding, 5 indifferent and 3 transient
16 transitions:
12 input and 4 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 r1 d g0 g1 /
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):
3
• Order-Independent input (Yinp)
• Order-Independent output (Yout)
• Output refusal sets do NOT propagate backward over inputs in state(s):
1 2
• 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 ]
01234567
0:01122334

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

Shortest paths from initial state:
0: r0 r1 r0 r1 r0 g0 r0 r1 g0 r0 r1 g1 r0 r1 g0 r0

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[c]
0:1[1]
1:2[3]
2:2[5]
3:2[7]
4:1[8]
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### Autocomparison Matrix

There are no state pairs (x,y) where x refines y outside the diagonal.

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### XDI Validity

'RGD 1-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)