XDI analysis of FORK

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  2> (AND/IF_1.0
  3> (NFA 
  4>      (NAME FORK)
  5>      (INTERPRETATION Verhoeff/XDI)
  6>      (NOTE Generated by digg v1.0)
  7>      (SYMBOLS 
  8>               (a INPUT)
  9>               (b0 OUTPUT)
 10>               (b1 OUTPUT)
 11>               (b2 OUTPUT)
 12>      )
 13>      (STATES 
 14>         (0 BOX INITIAL)
 15>         (1 TRANSIENT)
 16>         (2 TRANSIENT)
 17>         (3 TRANSIENT)
 18>         (4 TRANSIENT)
 19>         (5 TRANSIENT)
 20>         (6 TRANSIENT)
 21>         (7 TRANSIENT)
 22>      )
 23>      (TRANSITIONS
 24>          (0 1 a)
 25>          (1 2 b0)
 26>          (1 3 b1)
 27>          (1 4 b2)
 28>          (2 7 b1)
 29>          (2 5 b2)
 30>          (3 7 b0)
 31>          (3 6 b2)
 32>          (4 5 b0)
 33>          (4 6 b1)
 34>          (5 0 b1)
 35>          (6 0 b0)
 36>          (7 0 b2)
 37>      )
 38> ))
-----------------------------------------------------------------------------

Statistics

4 symbols:

1 input and 3 output

8 states:

0 demanding, 1 indifferent and 7 transient

13 transitions:

1 input and 12 output

Automorphisms (symmetries)

There are 6 automorphisms.

Finest Semi-independent Partition

/ a b0 b1 b2 /

Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Z^inp)
• 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
0:	0	1	2	2	2	3	3	3

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

Shortest paths from initial state:

0:
1:	a
2:	a b0
3:	a b1
4:	a b2
5:	a b0 b2
6:	a b1 b2
7:	a b0 b1

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]

d:	h	[c]
0:	1	[1]
1:	1	[2]
2:	3	[5]
3:	3	[8]

Autocomparison Matrix

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

XDI Validity

'FORK' is a valid XDI specification.