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of the broadcast interaction pattern, in which messages are not addressed to
specific receivers but potentially to all agents populating the space.
Reaction defines the synchronous interaction among a set of agents charac-
terized by given states and types and pair-wise situated in adjacent sites (that
is, adjacent agents ). Synchronous interaction is a two-steps process. Reaction
among a set of agents takes place through the execution of a protocol introduced
in order to synchronize the set of autonomous agents. The synchronization pro-
tocol involves a set of adjacent agents. When an agent wants to react with the
set of its adjacent agents since their types satisfy some required condition, it
starts an agreement process whose output is the subset of its adjacent agents
that have agreed to react. An agent agreement occurs when the agent is not
involved in other actions or reactions and when its state is such that this specific
reaction could take place. The agreement process is followed by the synchronous
reaction of the set of agents that have agreed to it.
In order to define agent action set ( Actions τ ) let us consider an agent a
of type τ whose current position is site p and whose current state is s (i.e.
a = <s,p,τ > ). Moreover, p = <a,F p ,P p > where F p is the set of fields active
in p and P p is the set of sites adjacent to p . To define the four action above
outlined, we will use operators of the form action-condit-effect . action is an
expression of the form f ( x 1 ...x n ) where f specifies the action name and x i are
variables which can appear in condit and effect expressions. condit and effect
express respectively the set of conditions that must be verified in order to let
the agent execute the action, and the set of effects deriving from the execution
of the action. They are sets of atomic formula p ( a 1 ...a k ) where p is a predicate
of arity k and a i are either constants or variables. According to this syntax, the
four basic agent actions are:
1. action: trigger ( s,f i ,s )
condit: state ( s ) ,perceive ( f i )
effect: state ( s )
where state ( s ) and perceive ( f i ) are verified when the agent state is s , and
f i ∈ F p and Compare f i
= True (that is, the field f i is
active in p and agents of type τ in state s can perceive it). The effect of
a trigger action is a change in state of the agent according to the third
parameter.
2. action: transport ( p,f i ,q )
condit: position ( p ) ,empty ( q ) ,near ( p,q ) ,perceive ( f i )
effect: position ( q ) ,empty ( p )
where perceive ( f i ) has the same meaning as in trigger (), while position ( p ),
empty ( q ) and near ( p,q ) are verified when the agent position is p , q ∈ P p and
q = < ⊥,F q ,P q > (that is, q is a site adjacent to p and no agent is situated in
it). The effect of the execution of a transport action is the change in position
of the agent undertaking the action and, as a consequence, the change of
the local space where the agent is situated. Let us suppose that agent a has
executed a transport ( p,f i ,p ). This means that a has changed its position
from p to p (i.e. a = <s,p ,τ > ) and as a consequences sites p and p have
changed respectively to
c τ ( s ) · w f i ,t τ ( s )
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