Automata based formulation: Definitions

 A Chronobot is a 8-tuple (M, S, f, k, s₀, F, DB, Φ)

Where

M is a non-empty set of messages (the message space)

S is a non-empty set of states (the state space), S = S_c * D_s * D_a

Where

S_c is a nonempty set  of states of the Chronobot

D_s is a nonempty set of self-models of the Chronobot, and

D_a is a nonempty set of alien-models of the Chronobot

f :  S_c * (M * M)^* -> S_c is the state transition function. Given the current state of the Chronobot and the history of messages exchanged between the Chronobot initiating the bid and the Chronobots participating in the bidding process, f specifies the next state

k :  D_{s *}  D_a -> N is the knowledge distance function. Given the self-model of the Chronobot

and the set of all other alien models of Chronobots participating in the bidding process, k

specifies the knowledge distance between the negotiating entities

Φ :  D_{s *}  D_a -> D_s is the knowledge plane function. Given the self-model of the Chronobot

and the set of all other alien models of Chronobots participating in the bidding process,

when k, the knowledge distance between the negotiating entities exceeds threshold t,

the knowledge plane function is responsible for transferring to the higher plane of

knowledge

s₀ in S is the initial state of the Chronobot

F, a subset of S, is the nonempty set of final states

DB is the Database that stores the history of all the Chronobots involved in the Time/Knowledge Exchange