XDI analysis of 1-Bit Variable
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
Processing AND/IF input stream:
-----------------------------------------------------------------------------
1> (AND/IF_1.0
2> (NFA
3> (NAME 1-Bit Variable)
4> (INTERPRETATION Verhoeff/XDI)
5> (SYMBOLS
6> (w0 INPUT ) (w1 INPUT ) (a OUTPUT)
7> (r INPUT ) (v0 OUTPUT) (v1 OUTPUT)
8> )
9> (STATES
10> ( 0 INITIAL BOX)
11> ( 1 TRANSIENT)
12> ( 2 TRANSIENT)
13> ( 3 BOX)
14> ( 4 TRANSIENT)
15> ( 5 BOX)
16> ( 6 TRANSIENT)
17> ( 7 TRANSIENT)
18> ( 8 TRANSIENT)
19> ( 9 TRANSIENT)
20> (10 TRANSIENT)
21> (11 TRANSIENT)
22> (12 TRANSIENT)
23> (13 TRANSIENT)
24> (14 TRANSIENT)
25> (15 TRANSIENT)
26> (16 TRANSIENT)
27> (17 TRANSIENT)
28> (18 TRANSIENT)
29> (19 TRANSIENT)
30> )
31> (TRANSITIONS
32> ( 0 6 w0) ( 0 1 w1) ( 0 2 r)
33> ( 1 3 a) ( 1 4 r)
34> ( 2 12 w0) ( 2 4 w1) ( 2 5 v0) ( 2 3 v1)
35> ( 3 6 w0) ( 3 19 w1) ( 3 7 r)
36> ( 4 8 a) ( 4 1 v0) ( 4 19 v1)
37> ( 5 18 w0) ( 5 1 w1) ( 5 9 r)
38> ( 6 5 a) ( 6 12 r)
39> ( 7 12 w0) ( 7 11 w1) ( 7 3 v1)
40> ( 8 14 w0) ( 8 13 w1) ( 8 3 v0) ( 8 3 v1)
41> ( 9 15 w0) ( 9 4 w1) ( 9 5 v0)
42> (10 17 w0) (10 16 w1) (10 5 v0) (10 5 v1)
43> (11 7 a) (11 19 v1)
44> (12 10 a) (12 18 v0) (12 6 v1)
45> (13 8 a) (13 19 v0) (13 19 v1)
46> (14 10 a) (14 6 v0) (14 6 v1)
47> (15 9 a) (15 18 v0)
48> (16 8 a) (16 1 v0) (16 1 v1)
49> (17 10 a) (17 18 v0) (17 18 v1)
50> (18 5 a) (18 15 r)
51> (19 3 a) (19 11 r)
52> )
53> )
54> )
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-
- 6 symbols:
- 3 input and 3 output
- 20 states:
- 0 demanding, 3 indifferent and 17 transient
- 57 transitions:
- 23 input and 34 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
-
There are 2 automorphisms.
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
-
/ w0 w1 a / r v0 v1 /
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
- Maximally Transient
- Disabling inputs (Zinp) in state(s):
- 0 2 3 5 7 8 9 10
- Disabling outputs (Zout) in state(s):
- 2 4 8 10 12 13 14 16 17
- Order-Independent input (Yinp)
- Order-Dependent output (Yout) in state(s):
- 1 6
- Output refusal sets do NOT propagate backward over inputs in state(s):
- 7 9
- Output Non-Deterministic
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
- All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]
| | | | | | | | | | | | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
|---|
| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|
| 0: | 0 | 1 | 1 | 2 | 2 | 2 | 1 | 3 | 3 | 3 | 3 | 4 | 2 | 4 | 4 | 4 | 4 | 4 | 3 | 3 |
|---|
Initial state not reachable from 19 states: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
There are 37 state pairs where one state is unreachable from the other state.
- Shortest paths from initial state:
-
| 0: | |
|---|
| 1: | w1 |
|---|
| 2: | r |
|---|
| 3: | w1 a |
|---|
| 4: | w1 r |
|---|
| 5: | w0 a |
|---|
| 6: | w0 |
|---|
| 7: | w1 a r |
|---|
| 8: | w1 r a |
|---|
| 9: | w0 a r |
|---|
| 10: | w0 r a |
|---|
| 11: | w1 a w1 r |
|---|
| 12: | w0 r |
|---|
| 13: | w1 r a w1 |
|---|
| 14: | w1 r a w0 |
|---|
| 15: | w0 a w0 r |
|---|
| 16: | w0 r a w1 |
|---|
| 17: | w0 r a w0 |
|---|
| 18: | w0 a w0 |
|---|
| 19: | w1 a w1 |
|---|
- 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: | 4 | [ 8] |
|---|
| 3: | 6 | [14] |
|---|
| 4: | 6 | [20] |
|---|
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
-
- There are 20 state pairs (x,y) where x refines y outside the diagonal:
- (3[],0[]) (4\/,16\/) (5[],0[]) (7\/,2\/) (7\/,8\/) (9\/,2\/) (9\/,10\/) (11\/,4\/) (11\/,13\/) (11\/,16\/) (12\/,14\/) (13\/,4\/) (13\/,16\/) (15\/,12\/) (15\/,14\/) (15\/,17\/) (17\/,12\/) (17\/,14\/) (18\/,6\/) (19\/,1\/)
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity
-
'1-Bit Variable' 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)
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