2 research outputs found
Parikh Matrices and Strong M-Equivalence
Parikh matrices have been a powerful tool in arithmetizing words by numerical
quantities. However, the dependence on the ordering of the alphabet is
inherited by Parikh matrices. Strong M-equivalence is proposed as a canonical
alternative to M-equivalence to get rid of this undesirable property. Some
characterization of strong M-equivalence for a restricted class of words is
obtained. Finally, the existential counterpart of strong M-equivalence is
introduced as well.Comment: 10 pages. Revised version. preprin
Parikh matrices and Parikh Rewriting Systems
Since the introduction of the Parikh matrix mapping, its injectivity problem
is on top of the list of open problems in this topic. In 2010 Salomaa provided
a solution for the ternary alphabet in terms of a Thue system with an
additional feature called counter. This paper proposes the notion of a Parikh
rewriting system as a generalization and systematization of Salomaa's result.
It will be shown that every Parikh rewriting system induces a Thue system
without counters that serves as a feasible solution to the injectivity problem.Comment: 15 pages, preprin