A catalogue of automata,
tested before they’re listed.

Finite and ω-automata, pushdown and Turing machines, transducers — each with its diagram, its language and its formal definition, and each one click from your canvas.

64 machines · 6 collections · How they are checked

guess the penultimate 1, NFA. Every figure in the library is drawn from the machine’s own file.

Recently added

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BB(6) champion: runs longer than 2↑↑↑5 steps ITM · 6×2 Deterministic Added 28 Sept 2026Updated 28 Sept 2026 3-tape adder — one pass MTM · 3 states Tested · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 4-tape ALU — add, and, or, xor, not MTM · 8 states Tested · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 A halt nothing leads to ITM · 3×2 · never halts Deterministic Added 28 Sept 2026Updated 28 Sept 2026

Busy Beaver Hall of Fame

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BB(2) champion ITM · 2×2 · halts in 6 Deterministic Added 28 Sept 2026Updated 28 Sept 2026 BB(3) champion — most steps ITM · 3×2 · halts in 21 Deterministic Added 28 Sept 2026Updated 28 Sept 2026 BB(3) champion — most ones ITM · 3×2 · halts in 14 Deterministic Added 28 Sept 2026Updated 28 Sept 2026 BB(4) champion ITM · 4×2 · halts in 107 Deterministic Added 28 Sept 2026Updated 28 Sept 2026

Regular languages, start to finish

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even number of 1s DFA · 2 states Minimal · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 Binary divisibility by 5 DFA · 5 states Tested · Minimal · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 guess the penultimate 1 NFA · 4 states Added 28 Sept 2026Updated 28 Sept 2026 Keyword search: cat | car | cab NFA · 4 states Tested Added 28 Sept 2026Updated 28 Sept 2026

The ω-automata zoo

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Never two a's in a row DBA · 3 states Tested · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 Eventually always b DcoBA · 2 states Tested · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 Eventually always b, by priority DPA · 2 states Tested · Deterministic Added 28 Sept 2026Updated 28 Sept 2026 Infinitely often a NBA · 2 states Tested Added 28 Sept 2026Updated 28 Sept 2026

Collections

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Beyond regular Stacks, queues, counters and tapes: what each kind of memory buys. 10 machines · curated by @thethinkmachine Busy Beaver Hall of Fame The champions: for each size, the halting machine that runs longest from a blank tape. Every step count here was checked by running the machine to its halt. 7 machines · curated by @thethinkmachine Three ways to never halt One machine per non-halting proof the library can make: an exact cycle, a cycle that drifts along the tape, and a halt that can never be reached. 3 machines · curated by @thethinkmachine The ω-automata zoo All eight acceptance conditions × determinism: Büchi, co-Büchi, parity and weak, deterministic and not — and the languages that tell them apart. 8 machines · curated by @thethinkmachine Regular languages, start to finish DFAs, NFAs, ε-NFAs and two-way automata — the finite-memory machines, from the textbook classics to the showcase examples. 9 machines · curated by @thethinkmachine Machines that write Moore and Mealy machines, finite-state and pushdown transducers, and a two-way transducer that copies its input. 7 machines · curated by @thethinkmachine

Every machine

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64 machines