On the generation of powers by OS schemes (Q1116709)

We study the reproducing power of propagating OS schemes (\(\Sigma\),P). It is shown that for such schemes the following holds. (i) If \(| \Sigma | =3\) then \(x\Rightarrow^*x^ 2\) holds for al x if and only if \(x\Rightarrow^*x^ 2\) holds for all strings of length less than or equal to 6; (ii) if \(| \Sigma | \geq 4\) or \(k\geq 3\) then no bound \(n_ 0\) exists such that \(x\Rightarrow^*x^ k\) for \(| x| \leq n_ 0\) would imply \(x\Rightarrow^*x^ k\) for all x.