feat(Automata, LTS, and Turing): saturated multistep transitions, mapLabel for LTS, and Nondeterministic Turing Machines (NTM)#615
feat(Automata, LTS, and Turing): saturated multistep transitions, mapLabel for LTS, and Nondeterministic Turing Machines (NTM)#615fmontesi wants to merge 11 commits into
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| instance : Acceptor (SingleTapeNTM State Symbol) Symbol where | ||
| Accepts (m : SingleTapeNTM State Symbol) (xs : List Symbol) := | ||
| ∃ s ∈ m.start, ∃ c', c'.state ∈ m.accept ∧ m.MRed (Cfg.mk₁ s xs) c' | ||
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In order to complete the definition at least for complexity theory, it would be nice to have a definition of the sort
def ComputesInTimeAndSpace (tm : SingleTapeNTM State Symbol) (input output : List Symbol) (t s : Nat) := ...alternatively
def AcceptsInTimeAndSpace (tm : SingleTapeNTM State Symbol) (input : List Symbol) (t s : Nat) := ...
Shreyas4991
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Shreyas4991
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This PR seems fine to me. The only question is whether we shouldn't just define the basic operations as move, read, write, etc, as opposed to a single step transition.
Pro:
The TM can be programmed by a lean function that chains these operations
Possible Con:
We will have to count read, write, and move as separate operations. However this is a small constant factor blow up which has no meaningful consequences in complexity theory or computability theory.
Discussion Thread
| namespace Cslib.Computability.Turing.SingleTape | ||
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| /-- The transition labels used by a single-tape Turing Machine. -/ | ||
| structure TrLabel (State Symbol : Type*) where |
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This could be an inductive type. We can replace the transition function with the basic operations on a TM. For more discussion see Zulip thread for this PR
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This PR:
LTS.SMTrfor LTS, which correctly invokes tau-closure for empty strings.Both changes have been discussed at the last CSLib General Meeting and are part of a larger discussion towards integrating machine models and transition systems (postponed to later work).