# XDI analysis of Forked Join

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```Processing AND/IF input stream:
-----------------------------------------------------------------------------
1> (AND/IF_1.0
2>   (NFA
3>     (NAME Forked Join)
4>     (SYMBOLS
5>       (a INPUT) (b INPUT) (c OUTPUT) (d OUTPUT)
6>     )
7>     (STATES
8>       (0 INITIAL BOX)
9>       (1 BOX)
10>       (2 BOX)
11>       (3 TRANSIENT)
12>       (4 TRANSIENT)
13>       (5 TRANSIENT)
14>       (6 TRANSIENT)
15>       (7 TRANSIENT)
16>       (8 TRANSIENT)
17>       (9 TRANSIENT)
18>     )
19>     (TRANSITIONS
20>       (0 1 a) (0 2 b)
21>       (1 3 b)
22>       (2 3 a)
23>       (3 4 c) (3 5 d)
24>       (4 6 a) (4 8 b) (4 0 d)
25>       (5 7 a) (5 9 b) (5 0 c)
26>       (6 1 d)
27>       (7 1 c)
28>       (8 2 d)
29>       (9 2 c)
30>     )
31>   )
32> )
-----------------------------------------------------------------------------

Forked Join: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Forked Join: 1 warning, 0 errors.

```

### Statistics

4 symbols:
2 input and 2 output
10 states:
0 demanding, 3 indifferent and 7 transient
16 transitions:
8 input and 8 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Automorphisms (symmetries)

There are 4 automorphisms.
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Finest Semi-independent Partition

/ a b c d /
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• Disabling inputs (Zinp) in state(s):
4 5
• 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 ]
0123456789
0:0112334444

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

Shortest paths from initial state:
0: a b a b a b c a b d a b c a a b d a a b c b a b d b

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[ c]
0:11]
1:23]
2:14]
3:26]
4:4[10]
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

'Forked 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)