Basic Definition of Distributed Ealgebras

A distributed ealgebra Aconsists of the following:

• A finite indexed set of single-agent programs , called modules. The module names are static nullary function names.

• A vocabulary = Fun(A) which includes each Fun() - {Self} but does not contain Self. In addition, contains a unary function name Mod.

• A collection of -states, called initial states of A, satisfying the following conditions:
  • Different module names are interpreted as different elements.
  • There are only finitely many elements a such that, for some module name , Mod(a) = .

An element a is an agent at S if there is a module name such that S Mod(a) = ; the corresponding is the program Prog(a) of a , and Fun() is the vocabulary Fun(a) of a . Agent a is deterministic if Prog(a) is so.

is the reduct of S to vocabulary Fun(a) - {Self} expanded with Self, which is interpreted as a . Think about as the local state of agent a corresponding to the global state S . (It is not necessary to define local states via global states; see [GM] for example.)

An agent a can make a move at S by firing Prog(a) at and changing S accordingly. As a part of the move, a may create new agents, e.g., by importing reserve elements.

To perform a move of a deterministic agent a , fire Updates(a,S) = Updates(Prog(a), ). Runs of a distributed ealgebra are defined below.

• Cooperative Actions