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State Transition Diagram (STD)

A graphical representation showing all possible states and the transitions between them based on inputs. It defines the system's behavior over time, crucial for finite state machine (FSM) design.
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The statement of the theorem

Let SS be the finite set of states, S=QS = Q. Define the input alphabet Σ\Sigma. The system behavior is defined by the transition function δ:Q×Σ→Q\delta: Q \times \Sigma \to Q. A transition from state qiq_i to qjq_j upon input xx is represented by the tuple (qi,x,qj)(q_i, x, q_j), such that qj=δ(qi,x)q_j = \delta(q_i, x). The system state at time t+1t+1 is Q(t+1)=δ(Q(t),X(t))Q(t+1) = \delta(Q(t), X(t)).