feat(Automata): Two-way automaton - #834
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| automaton can move from state `q` to state `q'` and move its head according to `m`. -/ | ||
| Tr (q : State) (x : Symbol) (m : SignType) (q' : State) : Prop | ||
| /-- The set of initial states of the automaton. -/ | ||
| start : Set State |
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Why do you want a set of starting and accepting states and not a single starting and single accpting state?
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That's just Vardi's definition. In the end, it doesn't really matter much, but this is also how NA is defined.
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This defines a (nondeterministic) two-way automaton, i.e. an automaton with an input tape that can move its input tape head in both directions, following the definition by [Vardi1989]. The purpose of introducing two-way automata is to prove the power of Turing machines with constant space following Vardi's proof of equivalence of two-way and one-way automata.
The definition is not via LTS mainly because the labels would not coincide with the input symbols, which makes it a bit more awkward. Instead, this defines a single-step relation between configurations and then
List.IsChainis used to define a "Run", e.g. a sequence of configurations such that adjacent ones are Step-related and which starts at an initial configuration.