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- MaxF: Choose the automata with the largest dependency set cardinality.
- MinF: The opposite of above.
In case W is not a singleton, the second stage H 2 is used to choose a single disjunctive
transition function δ i among W . In the experiment, the following shown heuristics can
significantly reduce the number of intermediate BDD nodes for some relatively large
problems.
- Reinforcement learning (R) [17]: Choose the best transition relation based on the
previous activity record.
- Reinforcement learning + Tabu (RT) [18]: Same as the reinforcement learning with
the difference that using tabu search for the selection policy.
Fig. 3. The two stage selection heuristics for the workset algorithm
5
Supervisor as Guards
As mentioned in Section 1, given a supervisor represented as a BDD, it is cumber-
some for the users to relate each state to the corresponding BDD variables. Therefore,
it is more convenient and natural to represent the supervisor in a form similar to the
original models. In this section, the guard generation procedure, originating from [8],
is discussed and combined with the BDD-based disjunctive partitioning approach in
Section 4.1.
The guard generation procedure, being dependent on three kinds of state sets, ex-
tracts a set of compact guards indicating under which conditions the event can be exe-
cuted without violating the specifications. These guards are then attached to the original
model to represent the supervisor.
5.1
Computation of the Basic State Sets
Concerning the states that are retained or removed after the synthesis process, the states
that enable an arbitrary event σ can be divided into three basic state sets : forbidden
state set, allowed state set and don't care state set.
The forbidden state set, denoted by Q f , is the set of states in the supervisor where
the execution of σ is defined for S 0 , but not for the supervisor. The allowed state set,
denoted by Q a , is the set of states in the supervisor where the execution of σ is defined
for the supervisor. In other word, for each event σ , Q a represents the set of states where
event σ must be allowed to be executed in order to end up in states belonging to the
supervisor.
In order to obtain compact and simplified guards, inspired from the Boolean mini-
mization techniques, another set of states, denoted by Q dc , which describes a situation
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