About Confusion Example

Alice's and Bob's example

Suppose that a concurrent and probabilistic system is composed by two agents: Alice and Bob.

Alice has to decide whether to go to city (50% of probability) or to stay at home (50% of probability).

Bob has to decide whether to go to theater alone (50% of probability) or with Alice (50% of probability). But this last option is only possible if she chooses to come to the city.

Alice's and Bob's example in Petri Net

The Alice's and Bob's example can be represented through Petri nets.

The initial state of the system in which Alice and Bob have made no decision yet is represented by tokens in the places Alice has to decide and Bob has to decide

The choices of Alice are represented by transitions that consume tokens from the place Alice has to decide,

while the choices of Bob are represented by transitions that consume tokens from the place Bob has to decide

Initially the transition representing the decision of Bob to go to cinema together to Alice is not enabled since Alice isn't in the city (no token in the place Alice is in the city)

Therefore, at the moment, Bob has the only possibility to go to cinema alone

Alice decides to go to city

After Alice decides to go to the city (a token reaches the place Alice is in city), the transition that represents the decision of Bob to go to cinema together to Alice is enabled.

Now Bob has all the options available, then he has 50% of probability both to decide to go to cinema alone and to decide to go to cinema together