On Word Equations in One Variable
For a word equation E of length n in one variable x occurring # x times in E a resolution algorithm of O ( n +# x log n ) time complexity is presented here. This is the best result known and for the equations that feature it yields time complexity of O ( n ) which is optimal. Additionally it is pro...
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| Veröffentlicht in: | Algorithmica 2011-08, Vol.60 (4), p.819-828 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For a word equation
E
of length
n
in one variable
x
occurring #
x
times in
E
a resolution algorithm of
O
(
n
+#
x
log
n
) time complexity is presented here. This is the best result known and for the equations that feature
it yields time complexity of
O
(
n
) which is optimal. Additionally it is proven here that the set of solutions of any one-variable word equation is either of the form
F
or of the form
F
∪(
uv
)
+
u
where
F
is a set of
O
(log
n
) words and
u
,
v
are some words such that
uv
is a primitive word. |
|---|---|
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-009-9375-3 |