Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 63 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.24.0-rc1

Da acc lang compl

Automata.da_acc_lang_compl

Plain-language statement

For a DA, complementing the language it accepts can be achieved by simply complementing the set of accepting states.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

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.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Da acc omega lang

Automata.da_acc_omega_lang

Plain-language statement

The ω-language accepted by a deterministic Buchi automaton is the ω-limit of the language accepted by the same automaton.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Da concat det run 2

Automata.da_concat_det_run_2

Plain-language statement

If any M2 copy in the second state component of M1.Concat acc1 M2 ever stabilizes (in the sense of never being deactivated from some point on), then it contains an infinite run of M2 starting from its activation.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Da concat det run cnt2

Automata.da_concat_det_run_cnt2

Plain-language statement

The second state component of M1.Concat acc1 M2 always has at least one inactive copy of M2 available.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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Project-declaredLean 4.24.0-rc1

Da concat of muller accept

Automata.da_concat_of_muller_accept

Plain-language statement

Any infinite word accepted by M1.Concat acc1 M2 under the Muller condition consists of a finite word accepted by M1 followed by an infinite word accepted by M2 under the Muller condition.

automata theoryformal languagescomputer science

Source project: Automata Theory

Person-level attribution pending.

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