XDI analysis of Forked Join

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

Automorphisms (symmetries)

There are 4 automorphisms.

Finest Semi-independent Partition

/ a b c d /

Choice, Order Dependence, Nondeterminism

• Maximally Transient
• Disabling inputs (Z^inp) in state(s):

  4 5

• No Disabling Outputs (Z^out)
• Order-Independent input (Y^inp)
• Order-Independent output (Y^out)
• Output refusal sets propate backward over inputs
• Output Deterministic

Distances

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

	0	1	2	3	4	5	6	7	8	9
0:	0	1	1	2	3	3	4	4	4	4

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

Shortest paths from initial state:

0:
1:	a
2:	b
3:	a b
4:	a b c
5:	a b d
6:	a b c a
7:	a b d a
8:	a b c b
9:	a b d b

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:	1	[ 4]
3:	2	[ 6]
4:	4	[10]

Autocomparison Matrix

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

XDI Validity

'Forked Join' is a valid XDI specification.