Definition 1. A state of an agent X is a tuple S(X) = (am(X), pc(X), ci(X), pv(X)), where:

• am(X) is agent mode,
• pc(X) is program counter,
• ci(X) is context information list,
• pv(X) is parameters values.

If necessary am, pc, ci, pv will be indicated by indexes S, S' etc. to point out the state they refer to.

All possible modes and transitions among them, for α^0 system layer, are shown in Fig. 1.

• Finished (F) means that an agent has finished its work.
• Init (I) is the default mode for agents that are inactive in the initial state.
• Running (X) means that an agent is performing one of its statements.
• Taken (T) means that one of the passive agent procedures has been called and the agent is executing it.
• For passive agents, waiting (W) means that the corresponding agent is inactive and waits for another agent to call one of its accessible procedures. For active agents, the mode means that the corresponding agent is waiting either for a communication with another active agent, or for a currently inaccessible procedure of a passive agent.

Fig. 1. Possible transitions among modes: a) active agents, b) passive agents.

The program counter points out the current statement of an agent i.e. the next statement to be executed or the statement that has been already executed by an agent but needs a feedback from another agent to be completed (e.g. a communication between agents). For active agents in the init or finished mode and for passive agents in the waiting mode, the program counter is equal to 0.

We say that:

• pc(X) points out an exec (exit, jump, null, start) statement iff the next statement to be executed is an exec (exit, jump, null, start) statement;
• pc(X) points out an if statement iff the next statement to be executed is the evaluating of the guard and entering one of the if statement alternatives;
• pc(X) points out a loop statement iff the next statement to be executed is the evaluating of the guard (if any) and possibly entering the loop statement;
• pc(X) points out a select statement iff the next statement to be executed is entering the select statement and possibly one of its branches;
• pc(X) points out an in or out statement iff the next statement to be executed is an in or out statement or the last executed statement is in or out and the agent is waiting for the communication to be completed (either with an active or a~passive agent).

The context information list contains additional information about the current state of an agent e.g. if an agent is in the waiting mode, ci contains information about events the agent is waiting for. Possible entries put into ci lists are given in Table 1. If an agent is in the init or finished mode, its context information list is empty.

Table 1. Relationships between the mode and the context information list of an agent.

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