  In this paper we propose a new, more appropriate definition of regular and
indeterminate strings. A regular string is one that is "isomorphic" to a string
whose entries all consist of a single letter, but which nevertheless may itself
include entries containing multiple letters. A string that is not regular is
said to be indeterminate. We begin by proposing a new model for the
representation of strings, regular or indeterminate, then go on to describe a
linear time algorithm to determine whether or not a string $x = x[1..n]$ is
regular and, if so, to replace it by a lexicographically least (lex-least)
string $y$ whose entries are all single letters. Furthermore, we connect the
regularity of a string to the transitive closure problem on a graph, which in
our special case can be efficiently solved. We then introduce the idea of a
feasible palindrome array MP of a string, and prove that every feasible MP
corresponds to some (regular or indeterminate) string. We describe an algorithm
that constructs a string $x$ corresponding to given feasible MP, while ensuring
that whenever possible $x$ is regular and if so, then lex-least. A final
section outlines new research directions suggested by this changed perspective
on regular and indeterminate strings.
