XDI analysis of Join

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME Join)
  4>     (INTERPRETATION Verhoeff/XDI)
  5>     (SYMBOLS 
  6>       (a INPUT)
  7>       (b INPUT)
  8>       (c OUTPUT)
  9>     )
 10>     (STATES
 11>       (0 INITIAL BOX)
 12>       (1 BOX)
 13>       (2 BOX)
 14>       (3 TRANSIENT)
 15>     )
 16>     (TRANSITIONS
 17>       (0 1 a)
 18>       (0 2 b)
 19>       (1 3 b)
 20>       (2 3 a)
 21>       (3 0 c)
 22>     )
 23>   )
 24> )
-----------------------------------------------------------------------------

Statistics

3 symbols:

2 input and 1 output

4 states:

0 demanding, 3 indifferent and 1 transient

5 transitions:

4 input and 1 output

Automorphisms (symmetries)

0:	a	b	c
0:	b	a	c

Finest Semi-independent Partition

/ a b c /

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
0:	0	1	1	2

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

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]

Autocomparison Matrix

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

XDI Validity

'Join' is a valid XDI specification.