Actors for the Ackermann machine (II) Pure communication.

Continues from Actors for the Ackermann machine . In this post we see the first interaction between the actors.

Notations: each actor a has an address :a and a stack a^{*}.

Let the play begin. The cast is the following:

ack_7

At the beginning of the performance, the actors are in the following configuration

ack_8

Only a with b can interact (i.e. the only moves in GLC which may happen between actors are those between the mentioned ones). Their interaction is a form of pure communication (via the graphic beta move). Two such moves are possible, in succession. This is described in the next figure, along with the changes in the actors configuration.

ack_9

The performance is thrilling: the actor a is almost exhausted after forcing  the actor b to drop down his mask.  In the process  a lost his friends  d and f (with his buddy e) in favour of b.  Only c is still taking the side of a.   What will happen next?

At this stage, no other interaction is possible without revealing what b is really thinking (what’s in his stack b^{*}). The first act is over.

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