XDI analysis of Quick-Return Linkage

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME Quick-Return Linkage)
  4>     (SYMBOLS
  5>       (a INPUT)
  6>       (b OUTPUT)
  7>       (c OUTPUT)
  8>       (d INPUT)
  9>     )
 10>     (STATES
 11>       (0 INITIAL BOX)
 12>       (1 TRANSIENT)
 13>       (2 BOX)
 14>       (3 TRANSIENT)
 15>       (4 BOX)
 16>       (5 TRANSIENT)
 17>       (6 TRANSIENT)
 18>       (7 TRANSIENT)
 19>       (8 TRANSIENT)
 20>       (9 BOX)
 21>       (10 TRANSIENT)
 22>       (11 BOX)
 23>     )
 24>     (TRANSITIONS
 25>       (0 1 a)
 26>       (1 2 c)
 27>       (2 3 d)
 28>       (3 4 b)
 29>       (4 5 a)
 30>       (5 6 b) (5 7 c)
 31>       (6 8 a) (6 9 c)
 32>       (7 9 b) (7 10 d)
 33>       (8 11 c)
 34>       (9 11 a) (9 0 d)
 35>       (10 0 b)
 36>       (11 1 d)
 37>     )
 38>   )
 39> )
-----------------------------------------------------------------------------

Quick-Return Linkage: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Quick-Return Linkage: 1 warning, 0 errors.

Statistics

4 symbols:

2 input and 2 output

12 states:

0 demanding, 5 indifferent and 7 transient

16 transitions:

8 input and 8 output

Automorphisms (symmetries)

There is 1 automorphism.

Finest Semi-independent Partition

/ a b / c d /

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 ]

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

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

Shortest paths from initial state:

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

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:	1	[ 3]
3:	1	[ 4]
4:	1	[ 5]
5:	1	[ 6]
6:	2	[ 8]
7:	3	[11]
8:	1	[12]

Autocomparison Matrix

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

XDI Validity

'Quick-Return Linkage' is a valid XDI specification.