# XDI analysis of Test-and-set

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 Test-and-set)
4>     (SYMBOLS
5>       (r INPUT) (t INPUT) (t0 OUTPUT) (t1 OUTPUT)
6>     )
7>
8>     (STATES
9>       (0 INITIAL BOX)
10>       (1 BOX)
11>       (2 TRANSIENT)
12>       (3 TRANSIENT)
13>     )
14>     (TRANSITIONS
15>       (0 1 r) (0 2 t)
16>       (1 3 t)
17>       (2 3 r)
18>       (2 0 t1)
19>       (3 0 t0)
20>       (3 1 t1)
21>     )
22>   )
23> )
-----------------------------------------------------------------------------

Test-and-set: warning: interpretation not given. Assuming 'Verhoeff/XDI'
Test-and-set: 1 warning, 0 errors.

```

### Statistics

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

### Automorphisms (symmetries)

 0: r t t0 t1
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Finest Semi-independent Partition

/ r t t0 t1 /
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Choice, Order Dependence, Nondeterminism

• Maximally Transient
• No Disabling Inputs (Zinp)
• Disabling outputs (Zout) in state(s):
3
• Order-Independent input (Yinp)
• Order-Independent output (Yout)
• Output refusal sets do NOT propagate backward over inputs in state(s):
2
• Output Non-Deterministic
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Distances

All states are reachable from the initial state:
[ + == 9 < distance < +inf , . == distance = +inf ]
0123
0:0112

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

Shortest paths from initial state:
0: r t r t

Distribution of distances from initial state:
[d=distance, h=occurrence count, c=cumulative occurrence count]
d:h[c]
0:1[1]
1:2[3]
2:1[4]
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Autocomparison Matrix

There are 2 state pairs (x,y) where x refines y outside the diagonal:
(0[],1[]) (2\/,3\/)
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### XDI Validity

'Test-and-set' 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 2.1.1 (Jun 26 1998 10:51:42)