# XDI analysis of 3-Join

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```Processing AND/IF input stream:
-----------------------------------------------------------------------------
2> (AND/IF_1.0
3> (NFA
4>      (NAME 3-Join)
5>      (INTERPRETATION Verhoeff/XDI)
6>      (NOTE Generated by digg v1.0)
7>      (SYMBOLS
8>               (a0 INPUT)
9>               (a1 INPUT)
10>               (a2 INPUT)
11>               (b OUTPUT)
12>      )
13>      (STATES
14>         (0 BOX INITIAL)
15>         (1 BOX)
16>         (2 BOX)
17>         (3 BOX)
18>         (4 BOX)
19>         (5 BOX)
20>         (6 TRANSIENT)
21>         (7 BOX)
22>      )
23>      (TRANSITIONS
24>          (0 1 a0)
25>          (0 2 a1)
26>          (0 3 a2)
27>          (1 7 a1)
28>          (1 4 a2)
29>          (2 7 a0)
30>          (2 5 a2)
31>          (3 4 a0)
32>          (3 5 a1)
33>          (4 6 a1)
34>          (5 6 a0)
35>          (6 0 b)
36>          (7 6 a2)
37>      )
38> ))
-----------------------------------------------------------------------------

```

### Statistics

4 symbols:
3 input and 1 output
8 states:
0 demanding, 7 indifferent and 1 transient
13 transitions:
12 input and 1 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Automorphisms (symmetries)

There are 6 automorphisms.
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Finest Semi-independent Partition

/ a0 a1 a2 b /
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### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Zinp)
• No Disabling Outputs (Zout)
• Order-Independent input (Yinp)
• Order-Independent output (Yout)
• Output refusal sets propate backward over inputs
• Output 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
0:01112232

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

Shortest paths from initial state:
0: a0 a1 a2 a0 a2 a1 a2 a0 a1 a2 a0 a1

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[c]
0:1[1]
1:3[4]
2:3[7]
3:1[8]
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Autocomparison Matrix

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

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### XDI Validity

'3-Join' 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)
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