`automaton``.is_valid`

A careful analysis of automata with spontaneous transitions shows that in some case, spontaneous-cycles may result in automata with an undefined behavior. They are called invalid.

Preconditions:

None

Examples



In [1]:

    
import vcsn









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.

The following examples are taken from lombardy.2013.ijac.

Automaton $\mathcal{Q}_3$ (Fig. 2) (in $\mathbb{Q}$)

The following automaton is invalid.



In [2]:

    
%%automaton q3
context = "lan_char, q"
$ -> 0
0 -> 0 <-1/2>\e
0 -> 1  <1/2>\e
1 -> 1 <-1/2>\e
1 -> 0  <1/2>\e
0 -> $



In [3]:

    
q3.is_valid()









    Out[3]:





False

Automaton $\mathcal{Q}_4$ (Fig. 3) (in $\mathbb{Q}$)

The following one, however, is valid. Spontaneous transitions can be eliminated.



In [4]:

    
%%automaton q4
context = "lan_char, q"
$ -> 0
0 -> 1 <1/2>\e, a
1 -> 0 <-1>\e, b
1 -> $ <2>



In [5]:

    
q4.proper()









    Out[5]:

An Invalid Thompson Automaton (Fig. 5)

Sadly enough, the (weighted) Thompson construction may build invalid automata from valid expressions.



In [6]:

    
e = vcsn.context('lal_char, q').expression('(a*+<-1>b*)*')
e.is_valid()









    Out[6]:





True



In [7]:

    
t = e.thompson()
t









    Out[7]:



In [8]:

    
t.is_valid()









    Out[8]:





False

automaton.is_valid

Examples

Automaton $\mathcal{Q}_3$ (Fig. 2) (in $\mathbb{Q}$)

Automaton $\mathcal{Q}_4$ (Fig. 3) (in $\mathbb{Q}$)

An Invalid Thompson Automaton (Fig. 5)

`automaton``.is_valid`