# XDI analysis of Join

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 Join)
4>     (INTERPRETATION Verhoeff/XDI)
5>     (SYMBOLS
6>       (a INPUT)
7>       (b INPUT)
8>       (c OUTPUT)
9>     )
10>     (STATES
11>       (0 INITIAL BOX)
12>       (1 BOX)
13>       (2 BOX)
14>       (3 TRANSIENT)
15>     )
16>     (TRANSITIONS
17>       (0 1 a)
18>       (0 2 b)
19>       (1 3 b)
20>       (2 3 a)
21>       (3 0 c)
22>     )
23>   )
24> )
-----------------------------------------------------------------------------

```

### Statistics

3 symbols:
2 input and 1 output
4 states:
0 demanding, 3 indifferent and 1 transient
5 transitions:
4 input and 1 output
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Automorphisms (symmetries)

 0: 0: a b c b a c
Top | Statistics | Automorphisms | Finest Semi-independent Partition | Choice, Order Dependence, Nondeterminism | Distances | Autocomparison | XDI Validity

### Finest Semi-independent Partition

/ a b c /
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)
• No Disabling Outputs (Zout)
• Order-Independent input (Yinp)
• Order-Independent output (Yout)
• Output refusal sets propate backward over inputs
• Output 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: a b a b

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

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

### XDI Validity

'Join' 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)