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https://github.com/meithecatte/busycoq
Busy Beaver deciders backed by Coq proof
https://github.com/meithecatte/busycoq
Last synced: 25 days ago
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Busy Beaver deciders backed by Coq proof
- Host: GitHub
- URL: https://github.com/meithecatte/busycoq
- Owner: meithecatte
- License: mit
- Created: 2023-07-26T21:30:12.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-07-22T12:08:23.000Z (5 months ago)
- Last Synced: 2024-07-22T14:28:02.710Z (5 months ago)
- Language: Coq
- Size: 326 KB
- Stars: 32
- Watchers: 6
- Forks: 5
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# BusyCoq
Verified implementations of [Busy Beaver deciders][decider]. The computation
is split into two parts:
- First, an untrusted decider, written in Rust, tries to decide whether
each machine halts. When it succeeds, it generates a *certificate*.
- Then, a *verifier*, proven correct in Coq and extracted to OCaml,
checks each certificate and makes sure that it is correct.
A Coq theorem guarantees that if the verifier accepts a certificate, then
the corresponding machine doesn't halt.
[decider]: https://bbchallenge.org/method#deciders
## Implemented deciders
- Cyclers
- Translated Cyclers
- Backwards Reasoning
- Bouncers
## Individual machines
Apart from deciders, the repository includes manual proofs for some machines
considered hard to decide automatically. At the moment, these include:
- [Skelet #1](https://www.sligocki.com/2023/03/13/skelet-1-infinite.html)
(due to the nature of the proof, the final computation is done by an
extracted OCaml program)
- [Skelet #10](https://www.sligocki.com/2023/03/14/skelet-10.html)
- [Skelet #15](https://www.sligocki.com/2023/02/05/shift-overflow.html)
- Skelet #26 (proof contributed by Jason Yuen; I am not aware of
the informal argument being outlined anywhere)
- [Skelet #33](https://discuss.bbchallenge.org/t/skelet-33-doesnt-halt-coq-proof/180)
(proof contributed by Jason Yuen)
- [Skelet #34](https://www.sligocki.com/2023/02/02/skelet-34.html)
- [Skelet #35](https://www.sligocki.com/2023/02/05/shift-overflow.html)
- the five "cubic-finned" machines analyzed by Justin Blanchard
(bbchallenge indices 7763480, 8120967, 10756090, 11017998, and 11018487).
## Running the deciders
Place the [seed database][seed] at `seed.dat` in the root of the repository.
Make sure you have Rust, Coq and OCaml installed. Then,
```bash
cd beaver
cargo build --release
time target/release/beaver decide ../seed.dat ../certs.dat
cd ../verify
make
time ./verify ../seed.dat ../certs.dat ../decided.dat
```
A binary file listing the database indices of all successfully decided machines
will be generated at `decided.dat`.
[seed]: https://bbchallenge.org/method#download
## Results
```
Cyclers:
11229238 Decided
0 OutOfSpace
3092791 OutOfTime
0 Halted
74342035 NotApplicable
Translated Cyclers:
73860624 Decided
0 OutOfSpace
481411 OutOfTime
0 Halted
3092791 NotApplicable
Backwards Reasoning:
2035576 Decided
979028 OutOfSpace
559598 OutOfTime
Bouncers:
1406032 Decided
23433 OutOfSpace
109161 OutOfTime
0 Halted
132594 Undecided
real 2m11.670s
user 25m32.012s
sys 0m3.364s
```
Here are some results from an earlier run with higher limits (50M steps,
64k tape cells) on the Translated Cyclers decider:
```
chikara:~/dev/busycoq/beaver$ \time target/release/beaver decide
Cyclers:
11229238 Decided
0 OutOfSpace
3092791 OutOfTime
0 Halted
74342035 NotApplicable
Translated Cyclers:
73861173 Decided
138452 OutOfSpace
342410 OutOfTime
0 Halted
3092791 NotApplicable
10784.09user 136.66system 15:12.51elapsed 1196%CPU (0avgtext+0avgdata 10180maxresident)k
0inputs+2794536outputs (0major+2590minor)pagefaults 0swaps
chikara:~/dev/busycoq/verify$ \time ./verify
79.89user 0.41system 1:20.32elapsed 99%CPU (0avgtext+0avgdata 124288maxresident)k
0inputs+664776outputs (0major+30600minor)pagefaults 0swaps
```