Da acc lang iff run acc
Automata.da_acc_lang_iff_run_acc
Plain-language statement
A finite word al is accepted by M if and only if M reaches an accepting state after running on al starting from the initial state.
Exact Lean statement
theorem da_acc_lang_iff_run_acc [Inhabited A] (M : DA A) (acc : Set M.State) (al : List A) :
al ∈ M.toNA.AcceptedLang acc ↔ M.RunOn al ∈ accFormal artifact
Lean source
theorem da_acc_lang_iff_run_acc [Inhabited A] (M : DA A) (acc : Set M.State) (al : List A) : al ∈ M.toNA.AcceptedLang acc ↔ M.RunOn al ∈ acc := by constructor · rintro ⟨n, as, ⟨ss, h_run, h_acc⟩, rfl⟩ have h0 := da_fin_run_unique h_run n (by omega) have h1 := da_run_on_of_det_run M as n simp [h1, ← h0, h_acc] · intro h_acc use al.length, al.padDefault ; simp [extract_padDefault] use (M.DetRun al.padDefault) ; constructor · exact da_fin_run_exists (M := M) al.length al.padDefault · simp [← da_run_on_to_det_run, h_acc]- Project
- Automata Theory
- License
- Apache-2.0
- Commit
- f196548710ce
- Source
- AutomataTheory/Automata/Det.lean:113-124
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Related declarations
Acc lang congr
acc_lang_congr
Plain-language statement
The language accepted by c.toDA with a unique accepting state s is exactly the equivalence class of s.
Source project: Automata Theory
Person-level attribution pending.
Acc lang concat e
Automata.acc_lang_concat_e
Plain-language statement
The language of the concatenation NA that is accepted by M0's accepting states is the language accepted by M0.
Source project: Automata Theory
Person-level attribution pending.
Acc lang concat ne
Automata.acc_lang_concat_ne
Plain-language statement
The language of the concatenation NA that is accepted by M1's accepting states is the language accepted by M0 concatenated with the language accepted by M1 minus the empty word.
Source project: Automata Theory
Person-level attribution pending.