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add "weak" and "inherently-weak" properties #22

Merged
merged 1 commit into from
Jun 2, 2014
Merged

add "weak" and "inherently-weak" properties #22

merged 1 commit into from
Jun 2, 2014

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adl
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@adl adl commented Jun 1, 2014

I would like to indicate in the property: line if an automaton is weak.

For Büchi automata, it is customary to distinguish two kinds of weakness:

  • weak Büchi automata are those in which, for each SCC, either all states are accepting, or all states are non-accepting
  • inherently weak automata are those whose SCCs do not mix accepting cycles with non-accepting cycles.

Of course any weak automaton is also inherently weak, and any inherently weak automaton can be converted to a weak automaton by adjusting the acceptance set.

Essentially, a weak automaton is one in which the acceptance condition could be specified in terms of SCCs (instead of transitions or states). Presented this way (please see the wording in 947375b) the "weak" property generalizes nicely to non-Büchi automata.

strejcek added a commit that referenced this pull request Jun 2, 2014
add "weak" and "inherently-weak" properties
@strejcek strejcek merged commit 876a324 into master Jun 2, 2014
This was referenced Jun 9, 2014
@adl adl deleted the weak branch June 10, 2014 07:44
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