# Edition, visualisation, traversal¶

## Weighted automata¶

In :
# We disable autosave for technical reasons.
# Replace 0 by 120 in next line to restore default.
%autosave 0

Autosave disabled

In :
import awalipy # If import fails, check that
# Python version used as Jupyter
# kernel matches the one
# Awalipy was compiled with.

[Warning] The python module awalipy relies on compilation executed "on-the-fly" depending on the context (type of weights, of labels, etc.). As a result, the very first call to a given function in a given context may take up to 10 seconds.


## Creating an weighted automaton or transducer¶

The constructor of both Transducer and Automaton take a second optional argument weightset of type str. Currently the weightsets implemented in awali are the following:

• "B" : the set {true, false}, endowed with and and or

• "Z" : the set of relative integers endowed with $+$ and $\times$

• "Q" : the set of rational numbers endowed with $+$ and $\times$
• "R" : the set of real numbers (double) endowed with $+$ and $\times$
• "C" : the set of complex numbers (pairs of double) endowed with $+$ and $\times$

• "Z-min-plus", set of relative integers endowed with $\min$ and $+$

• "Z-max-plus", set of relative integers endowed with $\max$ and $+$
• "R-max-prod", set of real numbers (double) endowed with $\max$ and $\times$

• "Z/kZ" (eg. "Z/3Z" "Z/99Z"), cyclic semiring of cardinal k, endowed with $+$ and $\times$

Creating an automaton over alphabet {0,1} and weightset Z.

In :
A = awalipy.Automaton("01", "Z")


Adding states is the same as for unweighted automata.

In :
stt_0 = A.add_state()


Transitions of weighted automata bear weights.

• The function set_transition takes an optional fourth argument of type str representing a weight.
• The function set_initial and set_final take an optional second argument of type str representing a weight.
In :
tr_0 = A.set_transition(stt_0,stt_0,"0","1")
tr_1 = A.set_transition(stt_0,stt_0,"1")        # Default "weight" parameter is the neutral element for multiplication.
tr_2 = A.set_transition(stt_0,stt_1,"1")        # In "Z" it is 1 and is not displayed.
tr_3 = A.set_transition(stt_1,stt_1,"0","2")
tr_4 = A.set_transition(stt_1,stt_1,"1","2")
A.display()


As may be seen above, weights are displayed between <...> and if a weight is the weightset multiplicative neutral element, then it is usually omitted.

In :
A.set_initial(stt_0,"1")
A.set_final(stt_1,"2")
A.display()


The methods starting with set_ or unset_ ignore an eventual previous weight. Awali also provides all the same commands starting with add_ which 1) add given weight to a transition, possibly creating it; and 2) returns the new weight of the transition and not its id.

In :
B = A.copy()
B.display()

11
100
1001


For bigger automata, it may be useful to look at the string representation of it.

In :
B

Out:
Automaton (lal_char_z):	Weight Set: Z	Alphabet: 01
States:{	0(i:1001)	1(f:2)	}
Transitions:{	0--<11>0-->0	0--1-->0	0--1-->1	1--<2>0-->1	1--<2>1-->1	1--<100>0-->0		}

NB: the mention "(i:1001)" following a state means that the state is initial with weight 1001. Similarly, "(f:2)" means final with weight 2.

## Epsilon transitions¶

As for unweighted automata, epsilon transitions are not allowed by default.

In :
C = A.allow_eps_transition()
C.display()


In :
stt_2 = C.add_state()
tr_6 = C.set_eps_transition(stt_2,stt_1)
tr_7 = C.set_transition(stt_1,stt_2,"\\e")
C.display()


## Deleting edges and states¶

Same as for boolean automata

Same as for boolean automata

## Access and traversal¶

Same as for unweighted automata, with a few extras

In :
B.display()


Functions src_of, dst_of and label_of work just as for boolean automata.

Getting the weight of a transition.

In :
B.weight_of(tr_0)  # tr_0 is the transition s0 --<11>0--> s1

Out:
'11'

Getting the initial/final weight of a state.

In :
B.get_initial_weight(stt_0), B.get_final_weight(stt_0)

Out:
('1001', '0')

Note also that the third parameter of unpack_transition(tr_id) is the weight.

In :
tr_content = B.unpack_transition(tr_6)
print (tr_content)
print ("source: "+str(tr_content))
print ("label: "+str(tr_content))
print ("weight: "+str(tr_content))
print ("destination: "+str(tr_content))

(1, '0', '100', 0)
source: 1
label: 0
weight: 100
destination: 0

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