How can automata compute logical operations such as AND, OR, and NOT?

In automata theory, logical operations are performed by elementary automata, or "logical organs," that process inputs based on binary states—typically represented as 1 (excited) or 0 (quiescent). By analyzing these states at a given time, automata can execute the three fundamental operations of language:1

• Conjunction (AND): The conjunction automaton receives two inputs ($N_1,N_2$) and produces an output of 1 only if both inputs are 1. For input pairs (0,0), (0,1), and (1,0), the output is 0; for (1,1), the output is 1.1
• Disjunction (OR): The disjunction automaton produces an output of 1 if at least one of the two inputs is 1. It registers an output of 0 only when both inputs are 0.1
• Negation (NOT): The negation automaton acts as a unary operator. By keeping one input ($N_1$) constantly excited, the automaton produces an output of 1 when the second input is 0, and an output of 0 when the second input is 1, effectively complementing the input value.1

These basic logical organs serve as the building blocks for constructing more complex systems and robots.1