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Example Models for APNN-ToolBox
This Net is divided into two sections(Left-section (refered as l) and Right-section (refered as r)).
The following algorithm is based on two flags and a token that is shared by the two sites l and r, and held by
one of l and r at any time (as in 13.5). The algorithm was first published in a programming notation.
The flag finished_l signals to the site_r that the site_l is presently not striving to become critical.
This allows the site_r to "easily" access its critical region, by the action p. Likewise, the flag finished_r,
allows the site_l to access its critical state, by the action f. The shared token alternates between at_l and at_r.
The step from pend1_l to pend2_l results in the token on at_l: by action c in case l obtains the token from at_r,
or by action d in case l held the token anyway. The step from pend1_r to pend2_r likewise results in the token
on at_r. Hence the token is always at the site that executed the step from pend1 to pend2 most recently.
After leaving quiet_l along the quiscent action a, the site_l takes three steps to reach its critical state critical_l.
In the first step, the fair action b brings l from pend0_l to pend1_l and removes the flag finished_l. Fairness of
b is local, because :b={pend0_l, finished_l} is local to l, with finished_l the only forward branching place in :b,
which is connected to the right site, r, by a loop (finished_l, p). The second step, from pend1_l to pend2_l, results
in the shared token on at_l,as described above. The third step brings l to critical_l, with action f in case site_r
signals with finished_r that it is presently not interested in going critical, or with action e in case the site_r
more recently executed the step from pend1_r to pend2_r. The algorithm's overall structure guarantees that one of
finished_r or at_ r will eventually carry a token that remains there until eventually either f or e occurs.
The two sites l and r are structurally symmetrical, but the initial state favors the right site.
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