Editing Openai/693343d7-a38c-8012-a67c-11cbed4c0fd9 (section)

====== An actor is a dynamical system AAA characterized by: ======
* State space SSS, which represents the possible configurations of the actor's properties.
* Transition function f(S,Ω,R,Π)f(S, \Omega, R, \Pi)f(S,Ω,R,Π), which governs how the actor changes state over time. - SSS: The actor's state at time ttt, - Ω\OmegaΩ: External influences or stimuli (for passive actors, Ω\OmegaΩ is often the primary driver of change), - RRR: Internal rules that govern the actor's behavior (for passive actors, RRR may be minimal or rule-based), - Π\PiΠ: The decision-making or policy of the actor (for agents, Π\PiΠ is central, representing goals, learning, and intention).

Mathematically:

St+1=f(St,Ωt,Rt,Πt)S_{t+1} = f(S_t, \Omega_t, R_t, \Pi_t)St+1=f(St,Ωt,Rt,Πt)
Where StS_tSt is the state of the actor at time ttt, and the transition depends on external inputs Ωt\Omega_tΩt, internal rules RtR_tRt, and the decisions made by the actor Πt\Pi_tΠt.