4 research outputs found
A Characterization of Morphic Words with Polynomial Growth
A morphic word is obtained by iterating a morphism to generate an infinite
word, and then applying a coding. We characterize morphic words with polynomial
growth in terms of a new type of infinite word called a .
A zigzag word is represented by an initial string, followed by a finite list of
terms, each of which repeats for each in one of three ways: it grows
forward [, backward [], or
just occurs once []. Each term can recursively contain subterms with their
own forward and backward repetitions. We show that an infinite word is morphic
with growth iff it is a zigzag word of depth . As corollaries,
we obtain that the morphic words with growth are exactly the ultimately
periodic words, and the morphic words with growth are exactly the
multilinear words
On D0L systems with finite axiom sets
We give a new solution for the language equivalence problem of D0L systems with finite axiom sets by using the decidability of the equivalence problem of finite valued transducers on HDT0L languages proved by Culik II and Karhumäki