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.
Recently added
All →
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
All 7 →
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
All 9 →
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
All 8 →
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
All 6 →
Beyond regular
Stacks, queues, counters and tapes: what each kind of memory buys.
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.
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.
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.
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.
Machines that write
Moore and Mealy machines, finite-state and pushdown transducers, and a two-way transducer that copies its input.
Every machine
64 machines
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
a* then b*
ε-NFA · 3 states
Added 28 Sept 2026Updated 28 Sept 2026
aⁿbⁿ
Counter · 3 states
Added 28 Sept 2026Updated 28 Sept 2026
aⁿbⁿ
DPDA · 3 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
aⁿbⁿcⁿ — beyond one stack
2PDA · 4 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
aⁿbⁿcⁿ with 2 tapes
MTM · 4 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
aⁿbⁿcⁿdⁿ — four counts, one stack of stacks
EPDA · 6 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Bank account: never overdrawn
Counter · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
BB(2,3) champion
ITM · 2×3 · halts in 38
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
BB(2,4) champion
ITM · 2×4 · halts in 3.93M
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
BB(2) champion
ITM · 2×2 · halts in 6
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(3) champion — most steps
ITM · 3×2 · halts in 21
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
BB(5) champion
ITM · 5×2 · halts in 47.2M
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
BB(6) champion: runs longer than 2↑↑↑5 steps
ITM · 6×2
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Binary → Gray code
FST · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Binary addition a+b
TM · 8 states · halts in 0
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Binary divisibility by 3
DFA · 3 states
Tested · 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
binary increment
TM · 3 states · halts in 2
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Bracket matcher ( ) [ ] { }
DPDA · 1 state
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Classic: aⁿbⁿ ↦ bⁿaⁿ
PDT · 3 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Classic: eventually always b
NBA · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Classic: Rabin's cut-point language
PFA · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Classic: reverse the input
2DFT · 4 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Combination lock: 1101
Moore · 5 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Copy twice: w ↦ ww
2DFT · 5 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Déjà vu: the last letter is a rerun
2NFA · 8 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
enqueue then match
QA · 3 states
Added 28 Sept 2026Updated 28 Sept 2026
even number of 1s
DFA · 2 states
Minimal · 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
Eventually always b, with a needless guess
NcoBA · 3 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Float regex, compiled
ε-NFA · 5 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
guess and check
2NFA · 4 states
Added 28 Sept 2026Updated 28 Sept 2026
guess the last 1
NDTM · 3 states
Added 28 Sept 2026Updated 28 Sept 2026
guess the penultimate 1
NFA · 4 states
Added 28 Sept 2026Updated 28 Sept 2026
Infinitely often a
NBA · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Infinitely often a, or eventually always c
NPA · 5 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Is n composite? Guess a factor
NDTM · 8 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Keyword search: cat | car | cab
NFA · 4 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
last-letter scan
2DFA · 5 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Marching right forever
ITM · 3×2 · never halts
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
mirrored string w·wʳ
NPDA · 3 states
Added 28 Sept 2026Updated 28 Sept 2026
Never two a's in a row
DBA · 3 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Never two a's, with a needless guess
NWA · 4 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Noisy channel: does it end in a?
PFA · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
nondeterministic rewriter
FST · 1 state
Added 28 Sept 2026Updated 28 Sept 2026
one step left
ITM · 2 states · halts in 1
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Palindromes in linear time
MTM · 5 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Palindromes: guess the middle
NPDA · 3 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Perfect copy: w#w
QA · 2 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
Powers of two, by halving
LBA · 6 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
report each bit
Mealy · 2 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Reverse the input
PDT · 3 states
Tested
Added 28 Sept 2026Updated 28 Sept 2026
scan to first b
LBA · 2 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Serial binary adder
Mealy · 2 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
traffic light
Moore · 3 states
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Two cells, forever
ITM · 3×2 · never halts
Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
Two passes, one head
2DFA · 5 states
Tested · Deterministic
Added 28 Sept 2026Updated 28 Sept 2026
two-stack handoff
2PDA · 4 states
Added 28 Sept 2026Updated 28 Sept 2026
No machine matchesTry fewer words or clear a filter — or build it and submit it, and it will be the first.