A protocol for dynamic gossip. Following (van Ditmarsch et al., 2017), a gossip protocol is defined as an epistemic formula using two agents. If this formula resolves to true, a call between these agents is allowed. If the formula resolves to false, such a call is not allowed. The first argument denotes the amount of agents, the second argument is the current knowledge structure, whereas the third argument denotes the call in question.

Converts a protocol to a string notation, as used in (van Ditmarsch et al., 2017).

The most simple and naive protocol, it allows any call to be made. φ(a,b) = ⊤

This protocol only allows a call if it leads to new secrets to be learned. φ(a,b) = ¬S(a,b)

Introduced by (van Ditmarsch et al., 2017): "Call xy can be made if x knows y's number and if x considers it possible that there is a secret known by one of x,y but not the other." φ(a,b) = ⋁_{z ∈ A}( S(x, z) ↔︎ ¬S(y, z) )

Selects all calls that are allowed by the given gossip protocol. Note that there could also be no calls allowed.