Language of matching parens

Recognition with a deterministic push-down automaton with one state ▷. To accept, final state must be ▷ only (stack to the left of ▷ is empty).

r1 : ▷ • [ ->> [ • ▷.
r2 : [ • ▷ • ] ->> ▷.

Examples

Success

%trace *
▷ • [ • [ • [ • ] • [ • [ • ] • ] • ] • ].

▷•[•[•[•]•[•[•]•]•]•]

[•▷•[•[•]•[•[•]•]•]•]

[•[•▷•[•]•[•[•]•]•]•]

[•[•[•▷•]•[•[•]•]•]•]

[•[•▷•[•[•]•]•]•]

[•[•[•▷•[•]•]•]•]

[•[•[•[•▷•]•]•]•]

[•[•[•▷•]•]•]

[•[•▷•]•]

[•▷•]

▷

Failure (too many right parens)

%trace *
▷ • [ • [ • ] • [ • [ • ] • ] • ] • ].

▷•[•[•]•[•[•]•]•]•]

[•▷•[•]•[•[•]•]•]•]

[•[•▷•]•[•[•]•]•]•]

[•▷•[•[•]•]•]•]

[•[•▷•[•]•]•]•]

[•[•[•▷•]•]•]•]

[•[•▷•]•]•]

[•▷•]•]

▷•]

Failure (too many left parens)

%trace *
▷ • [ • [ • [ • [ • [ • ] • ] • ] • ].

▷•[•[•[•[•[•]•]•]•]

[•▷•[•[•[•[•]•]•]•]

[•[•▷•[•[•[•]•]•]•]

[•[•[•▷•[•[•]•]•]•]

[•[•[•[•▷•[•]•]•]•]

[•[•[•[•[•▷•]•]•]•]

[•[•[•[•▷•]•]•]

[•[•[•▷•]•]

[•[•▷•]

[•▷