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DFA · Regular

Binary divisibility by 3

@thethinkmachine·version 1·CC BY 4.0·added 28 Sept 2026

Three states, one per remainder mod 3. Reading bit b takes remainder r to (2r + b) mod 3.

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r0r1r2011001
The machine as drawn — 3 states, 6 transitions.Every word up to length 8, one row per length in shortlex order, inked where it is accepted.

The author’s examples, run

ε → accept11 → accept110 → accept1001 → accept10 → reject111 → reject