-
formal languages,
shortlex is a
total ordering for
finite sequences of
objects that can
themselves be
totally ordered. In the
shortlex ordering, sequences...
- sequence. This
variant of the
lexicographical order is
sometimes called shortlex order. In
lexicographical order, the word "Thomas"
appears before "Thompson"...
- D 6 ∗ / ∼ {\displaystyle {\mathcal {D}}_{6}^{*}/\sim }
equipped with a
shortlex order,
where the
equivalence class ∼ {\displaystyle \sim } is { n ∈ D 6...
-
minimal element. See
Shortlex for an
alternative string ordering that
preserves well-foundedness. For the
example alphabet, the
shortlex order is ε < 0 <...
- some
recursive order. For instance, the
binary Champernowne sequence in
shortlex order is 0 1 00 01 10 11 000 001 ... (sequence A076478 in the OEIS) where...
- numerals, in
natural order of the
integers represented, is
automatically in
shortlex order (shortest first,
lexicographical within each length). Thus, using...
- {\displaystyle <}
among the
words generated by X {\displaystyle X} (e.g.,
shortlex order). For each
relation P i = Q i {\displaystyle P_{i}=Q_{i}} in R {\displaystyle...
-
setting the n th bit of the
sequence to 1 if and only if the n th
string (in
shortlex order) is in the language. This
representation is
useful in the diagonalization...
- 10\ 11\ 000\ 001\ldots }
formed by
concatenating all
binary strings in
shortlex order,
clearly contains all the
binary strings and so is disjunctive. (The...
- extra-large type are
biautomatic (David Peifer).
Artin groups of
large type are
shortlex automatic with
regular geodesics (Derek Holt and
Sarah Rees). Many other...
