XDI analysis of Resettable-Join

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME Resettable-Join)
  4>     (INTERPRETATION Verhoeff/XDI)
  5>     (SYMBOLS 
  6>       (a INPUT)
  7>       (b INPUT)
  8>       (c OUTPUT)
  9>       (r INPUT)
 10>       (k OUTPUT)
 11>     )
 12>     (STATES
 13>       (0 INITIAL BOX)
 14>       (1 BOX)
 15>       (2 BOX)
 16>       (3 BOX)
 17>       (4 TRANSIENT)
 18>       (5 TRANSIENT)
 19>     )
 20>     (TRANSITIONS
 21>       (0 1 a)
 22>       (0 2 b)
 23>       (0 3 r)
 24>       (1 5 b)
 25>       (1 4 r)
 26>       (2 5 a)
 27>       (2 4 r)
 28>       (3 4 a)
 29>       (3 4 b)
 30>       (4 0 k)
 31>       (5 0 c)
 32>     )
 33>   )
 34> )
-----------------------------------------------------------------------------

Statistics

5 symbols:

3 input and 2 output

6 states:

0 demanding, 4 indifferent and 2 transient

11 transitions:

9 input and 2 output

Automorphisms (symmetries)

There are 2 automorphisms.

Finest Semi-independent Partition

/ a b c r k /

Choice, Order Dependence, Nondeterminism

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

  1 2 3

• 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
0:	0	1	1	1	2	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:	r
4:	a r
5:	a b

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:	2	[6]

Autocomparison Matrix

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

XDI Validity

'Resettable-Join' is a valid XDI specification.