3.7.24. Automaton with same input symbol
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A constraint for which the catalogue provides an automaton belonging to the following category:
Symbols of the alphabet are split in two categories:
neutral ones and non-neutral ones.
Non-neutral symbols correspond to symbols occurring on transitions
between two distinct states, while neutral symbols correspond to all
the other symbols of the alphabet.
Self-loops labelled by a neutral symbol do not modify any counter.
Ignoring transitions labelled by neutral symbols,
every state has its incoming transitions labelled by the same non-neutral symbol.
Ignoring transitions labelled by neutral symbols, outgoing
transitions of a state are not labelled by the symbol associated
with its incoming non-loop transitions.
For such automata we define the semantics of a state
as the regular expression associated with the language fragment obtained
from entering state to just before leaving state .
As an example, consider the constraint and its
automaton depicted by FigureΒ 3.7.6. The alphabet
corresponds to the set of symbols from which and
are non-neutral symbols (i.e.,Β the symbols associated with the transitions
between states and ), and is a neutral symbol.
First there is no counter modification on all self-loops.
If we remove the self-loops carrying the neutral symbol we have that:
All incoming transitions in state are labelled by the non-symbol ,
and all outgoing transitions from state are not labelled by .
All incoming transitions in state are labelled by the non-symbol ,
and all outgoing transitions from state are not labelled by .
The corresponding state semantics is given by the upper-leftmost box.