XDI analysis of Initialized bit variable with arbitration

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Processing AND/IF input stream:
-----------------------------------------------------------------------------
  2> (AND/IF_1.0
  3> (NFA 
  4>      (NAME  Initialized bit variable with arbitration)
  5>      (INTERPRETATION Verhoeff/XDI)
  6>      (NOTE Generated by digg v1.0)
  7>      (SYMBOLS 
  8>               (w0 INPUT)
  9>               (w1 INPUT)
 10>               (r INPUT)
 11>               (v0 OUTPUT)
 12>               (v1 OUTPUT)
 13>               (a OUTPUT)
 14>      )
 15>      (STATES 
 16>         (0 BOX INITIAL)
 17>         (1 TRANSIENT)
 18>         (2 TRANSIENT)
 19>         (3 TRANSIENT)
 20>         (4 TRANSIENT)
 21>         (5 TRANSIENT)
 22>         (6 BOX)
 23>         (7 TRANSIENT)
 24>         (8 TRANSIENT)
 25>         (9 TRANSIENT)
 26>         (10 TRANSIENT)
 27>         (11 TRANSIENT)
 28>         (12 TRANSIENT)
 29>         (13 TRANSIENT)
 30>         (14 TRANSIENT)
 31>         (15 TRANSIENT)
 32>         (16 TRANSIENT)
 33>         (17 TRANSIENT)
 34>      )
 35>      (TRANSITIONS
 36>          (0 1 w0)
 37>          (0 2 w1)
 38>          (0 3 r)
 39>          (1 4 r)
 40>          (1 0 a)
 41>          (2 5 r)
 42>          (2 6 a)
 43>          (3 4 w0)
 44>          (3 5 w1)
 45>          (3 0 v0)
 46>          (4 1 v0)
 47>          (4 3 a)
 48>          (5 2 v0)
 49>          (5 8 v1)
 50>          (5 15 a)
 51>          (6 7 w0)
 52>          (6 8 w1)
 53>          (6 9 r)
 54>          (7 10 r)
 55>          (7 0 a)
 56>          (8 11 r)
 57>          (8 6 a)
 58>          (9 10 w0)
 59>          (9 11 w1)
 60>          (9 6 v1)
 61>          (10 1 v0)
 62>          (10 7 v1)
 63>          (10 12 a)
 64>          (11 8 v1)
 65>          (11 9 a)
 66>          (12 13 w0)
 67>          (12 14 w1)
 68>          (12 0 v0)
 69>          (12 0 v1)
 70>          (13 1 v0)
 71>          (13 1 v1)
 72>          (13 12 a)
 73>          (14 2 v0)
 74>          (14 2 v1)
 75>          (14 15 a)
 76>          (15 16 w0)
 77>          (15 17 w1)
 78>          (15 6 v0)
 79>          (15 6 v1)
 80>          (16 7 v0)
 81>          (16 7 v1)
 82>          (16 12 a)
 83>          (17 8 v0)
 84>          (17 8 v1)
 85>          (17 15 a)
 86>      )
 87> ))
-----------------------------------------------------------------------------


Statistics

6 symbols:
3 input and 3 output
18 states:
0 demanding, 2 indifferent and 16 transient
50 transitions:
18 input and 32 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity


Automorphisms (symmetries)

There are 2 automorphisms.
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity


Finest Semi-independent Partition

/ w0 w1 a / r v0 v1 /
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity


Choice, Order Dependence, Nondeterminism

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Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]
             11111111
   012345678901234567
 0:011122233344566344

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

Shortest paths from initial state:
 0:
 1:w0 
 2:w1 
 3:
 4:w0 r 
 5:w1 r 
 6:w1 a 
 7:w1 a w0 
 8:w1 r v1 
 9:w1 a r 
10:w1 a w0 r 
11:w1 r v1 r 
12:w1 r a w0 a 
13:w1 r a w0 a w0 
14:w1 r a w0 a w1 
15:w1 r a 
16:w1 r a w0 
17:w1 r a w1 

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[ c]
0:11]
1:34]
2:37]
3:4[11]
4:4[15]
5:1[16]
6:2[18]
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Autocomparison Matrix

There are 16 state pairs (x,y) where x refines y outside the diagonal:
(1\/,7\/) (3\/,12\/) (4\/,10\/) (4\/,13\/) (4\/,16\/) (5\/,14\/) (8\/,2\/) (9\/,15\/) (10\/,16\/) (11\/,5\/) (11\/,14\/) (11\/,17\/) (13\/,10\/) (13\/,16\/) (17\/,5\/) (17\/,14\/)
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XDI Validity

'Initialized bit variable with arbitration' is a valid XDI specification.

Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity


XDI State Graph Tool, Version 2.0 (Feb 17 1998 20:34:43)
Copyright © 1995-1997 Eindhoven University of Technology