Finite Automata Reduction
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Finite Automata Reduction (short FAR) is a co-CTL decider. It works by finding a regular language restricted to a class of Nondeterministic Finite Automata[1] containing all eventually halting configurations of a TM. If the empty tape is not in the regular language, the TM has been shown to be non-halting.
History
- In October 2022, Finite Automata Reduction was first introduced by Justin Blanchard.[2] Later in October, Konrad Deka developed an SAT-based FAR implementation.[3]
- In January 2023, Finite Automata Reduction was reproduced by Tony Guilfoyle.[4]
- In April 2023, the decider was added to the deciders write-up, becoming section 6. Later in April, it was also reproduced by Tristan Stérin.[5] On the 9th of April, Finite Automata Reduction was applied on the remaining BB(5) holdouts.[6]
See also
- Section 6 of bbchallenge's deciders write-up.
- Meet-in-the-Middle Weighted Finite Automata Reduction (MITMWFAR)
References
- ↑ https://arxiv.org/pdf/2509.12337 Determination of the fifth Busy Beaver value
- ↑ https://github.com/UncombedCoconut/bbchallenge-deciders/tree/finite-automata-reduction/decider-finite-automata-reduction
- ↑ https://github.com/colette-b/bbchallenge
- ↑ https://github.com/TonyGuil/bbchallenge/tree/main/FAR
- ↑ https://github.com/bbchallenge/bbchallenge-deciders/tree/main/decider-finite-automata-reduction-reproduction
- ↑ https://discuss.bbchallenge.org/t/decider-finite-automata-reduction/123