ProV Logo
0
On universal partial words
Chen, Herman Z. Q....

Free

On universal partial words by Chen, Herman Z. Q. ( Author )
Lemonjar Open Access
N.A
25-01-2016
A universal word for a finite alphabet A and some integer n≥1 is a word over A such that every word in An appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any A and n. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from A may contain an arbitrary number of occurrences of a special `joker' symbol ◊∉A, which can be substituted by any symbol from A. For example, u=0◊011100 is a linear partial word for the binary alphabet A={0,1} and for n=3 (e.g., the first three letters of u yield the subwords 000 and 010). We present results on the existence and non-existence of linear and cyclic universal partial words in different situations (depending on the number of ◊s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.
-
Article
pdf
36.88 KB
English
-
MYR 0.01
-
https://arxiv.org/abs/1601.06456
Share this eBook