XDI analysis of 3-Join

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

Automorphisms (symmetries)

There are 6 automorphisms.

Finest Semi-independent Partition

/ a0 a1 a2 b /

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	1	1	2	2	3	2

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

Shortest paths from initial state:

0:
1:	a0
2:	a1
3:	a2
4:	a0 a2
5:	a1 a2
6:	a0 a1 a2
7:	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]

Autocomparison Matrix

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

XDI Validity

'3-Join' is a valid XDI specification.