XDI comparison of PAR Element (DIAL) and PAR-Element

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  2> (AND/IF_1.0
  3> (NFA 
  4>      (NAME PAR Element (DIAL))
  5>      (INTERPRETATION Verhoeff/XDI)
  6>      (NOTE Generated by digg v1.0)
  7>      (SYMBOLS 
  8>               (ar INPUT)
  9>               (ba INPUT)
 10>               (ca INPUT)
 11>               (aa OUTPUT)
 12>               (br OUTPUT)
 13>               (cr OUTPUT)
 14>      )
 15>      (STATES 
 16>         (0 BOX INITIAL)
 17>         (1 TRANSIENT)
 18>         (2 TRANSIENT)
 19>         (3 TRANSIENT)
 20>         (4 TRANSIENT)
 21>         (5 BOX)
 22>         (6 BOX)
 23>         (7 BOX)
 24>         (8 TRANSIENT)
 25>         (9 TRANSIENT)
 26>      )
 27>      (TRANSITIONS
 28>          (0 1 ar)
 29>          (1 2 br)
 30>          (1 3 cr)
 31>          (2 9 ba)
 32>          (2 5 cr)
 33>          (3 4 ca)
 34>          (3 5 br)
 35>          (4 7 br)
 36>          (5 6 ba)
 37>          (5 7 ca)
 38>          (6 8 ca)
 39>          (7 8 ba)
 40>          (8 0 aa)
 41>          (9 6 cr)
 42>      )
 43> ))
-----------------------------------------------------------------------------

Processing AND/IF input stream:
-----------------------------------------------------------------------------
  1> (AND/IF_1.0
  2>   (NFA
  3>     (NAME PAR-Element)
  4>     (SYMBOLS 
  5>       (ar INPUT) (aa OUTPUT) (br OUTPUT) (ba INPUT)
  6>       (cr OUTPUT) (ca INPUT)
  7>     )
  8> 
  9>     (STATES
 10>       (0 INITIAL BOX)
 11>       (1 TRANSIENT)
 12>       (2 TRANSIENT)
 13>       (3 TRANSIENT)
 14>       (4 TRANSIENT)
 15>       (5 BOX)
 16>       (6 TRANSIENT)
 17>       (7 BOX)
 18>       (8 BOX)
 19>       (9 TRANSIENT)
 20>     )
 21>     (TRANSITIONS
 22>       (0 1 ar)
 23>       (1 2 br) (1 3 cr)
 24>       (2 4 ba) (2 5 cr)
 25>       (3 5 br) (3 6 ca)
 26>       (4 7 cr)
 27>       (5 7 ba) (5 8 ca)
 28>       (6 8 br)
 29>       (7 9 ca)
 30>       (8 9 ba)
 31>       (9 0 aa)
 32>     )
 33>   )
 34> )
-----------------------------------------------------------------------------

(AND/IF_1.0 
(NFA 
     (NAME PAR Element (DIAL))
     (INTERPRETATION Verhoeff/XDI)
     (NOTE Generated by digg v1.0)
     (SPAR-Element: warning: interpretation not given. Assuming 'Verhoeff/XDI'
PAR-Element: 1 warning, 0 errors.

Alphabets

'PAR Element (DIAL)' and 'PAR-Element' have comparable alphabets

Joint Reachability

# reachable state pairs = 10
[ + == 9 < distance < +inf , . == distance = +inf ]

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

Shortest distances and paths from initial pair

[(s,t)=state pair, d=distance, X\Y=not indiv. min., path=shortest path]

(s,t):	d,	X\Y,	path
(0,0):	0,	\ ,
(1,1):	1,	\ ,	ar
(2,2):	2,	\ ,	ar br
(3,3):	2,	\ ,	ar cr
(4,6):	3,	\ ,	ar cr ca
(5,5):	3,	\ ,	ar br cr
(6,7):	4,	\ ,	ar br ba cr
(7,8):	4,	\ ,	ar br cr ca
(8,9):	5,	\ ,	ar br ba cr ca
(9,4):	3,	\ ,	ar br ba

Distribution of distances from initial pair

[d=distance, h=occurrence count, c=cumulative occurrence count]

d:	h	[ c]
0:	1	[ 1]
1:	1	[ 2]
2:	2	[ 4]
3:	3	[ 7]
4:	2	[ 9]
5:	1	[10]

Comparison

'PAR Element (DIAL)' refines 'PAR-Element'.

Comparison Matrix:

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

'PAR Element (DIAL)' is refined by 'PAR-Element'.
Comparison Matrix:

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