Switching Theory

digital-logic computation

Definition

Switching Theory

Switching theory is the mathematical study of systems built from components that switch between finitely many discrete states, usually $0$ and $1$. A combinational switching system computes a Boolean function

$$f:\{0,1{\}}^n\to \{0,1{\}}^m,$$

and switching theory studies how to represent, simplify, and realise $f$ using switches or digital circuits. For systems with memory, it also studies state transitions

$$q_{t+1}=F(q_t,x_t),y_t=G(q_t,x_t),$$

where $q_t$ is the current state, $x_t$ the input, and $y_t$ the output. Boolean algebra provides its principal symbolic language.